Factoring Rational Expressions - Algebra 2
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Simplify:
Simplify:
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If we factors the denominator we get
Hence the rational expression becomes equal to
which is equal to 
If we factors the denominator we get
Hence the rational expression becomes equal to
which is equal to
Simplify:
Simplify:
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First factor the numerator. We need two numbers with a sum of 3 and a product of 2. The numbers 1 and 2 satisfy these conditions:
Now, look to see if there are any common factors that will cancel:
The 
in the numerator and denominator cancel, leaving 
.
First factor the numerator. We need two numbers with a sum of 3 and a product of 2. The numbers 1 and 2 satisfy these conditions:
Now, look to see if there are any common factors that will cancel:
The
Simplify.
Simplify.
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a. Simplify the numerator and denominator separately by pulling out common factors.
b. Reduce if possible.
c. Factor the trinomial in the numerator.
d. Cancel common factors between the numerator and the denominator.
a. Simplify the numerator and denominator separately by pulling out common factors.
b. Reduce if possible.
c. Factor the trinomial in the numerator.
d. Cancel common factors between the numerator and the denominator.
Transform the following equation from standard into vertex form:
Transform the following equation from standard into vertex form:
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To take this standard form equation and transform it into vertex form, we need to complete the square. That can be done as follows:
We will complete the square on 
. In this case, our 
in our soon-to-be 
is 
. We therefore want our 
, so 
.
Since we are adding 
on the right side (as we are completing the square inside the parentheses), we need to add 
on the left side as well. Our equation therefore becomes:
Our final answer is therefore 
To take this standard form equation and transform it into vertex form, we need to complete the square. That can be done as follows:
We will complete the square on
Since we are adding
Our final answer is therefore
Evaluate the following expression: 
Evaluate the following expression:
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When we multiply expressions with exponents, we need to keep in mind some rules:
Multiplied variables add exponents.
Divided variables subtract exponents.
Variables raised to a power multiply exponents.
Therefore, when we mulitiply the two fractions, we obtain:
Our final answer is therefore 
When we multiply expressions with exponents, we need to keep in mind some rules:
Multiplied variables add exponents.
Divided variables subtract exponents.
Variables raised to a power multiply exponents.
Therefore, when we mulitiply the two fractions, we obtain:
Our final answer is therefore
Simplify this rational expression: 
Simplify this rational expression:
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To see what can be simplified, factor the quadratic equations.
Cancel out like terms:
Combine terms:
To see what can be simplified, factor the quadratic equations.
Cancel out like terms:
Combine terms:
Simplify the rational expression by factoring:
Simplify the rational expression by factoring:
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To simplify it is best to completely factor all polynomials:
Now cancel like terms:
Combine like terms:
To simplify it is best to completely factor all polynomials:
Now cancel like terms:
Combine like terms:
Factor and simplify this rational expression: 
Factor and simplify this rational expression:
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Completely factor all polynomials:
Cancel like terms:
Completely factor all polynomials:
Cancel like terms:
Factor 
.
Factor
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In the beginning, we can treat this as two separate problems, and factor the numerator and the denominator independently:
After we've factored them, we can put the factored equations back into the original problem:
From here, we can cancel the 
from the top and the bottom, leaving:
In the beginning, we can treat this as two separate problems, and factor the numerator and the denominator independently:
After we've factored them, we can put the factored equations back into the original problem:
From here, we can cancel the
Factor: 
Factor:
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Factor a two out in the numerator.
Factor the trinomial.
Factor the denominator.
Divide the terms.
The answer is: 
Factor a two out in the numerator.
Factor the trinomial.
Factor the denominator.
Divide the terms.
The answer is:
Simplify to simplest terms.
Simplify to simplest terms.
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The correct answer is 
. The numerator and denominator can both be factored to simpler terms:
The 
terms will cancel out. Leaving 
. While this is an answer choice, it can be simplified further. Factoring out a 
from the denominator will allow the 
terms to cancel out leaving 
.
The correct answer is
The
Simplify:
Simplify:
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If we factors the denominator we get
Hence the rational expression becomes equal to
which is equal to
If we factors the denominator we get
Hence the rational expression becomes equal to
which is equal to
Simplify:
Simplify:
Tap to see back →
First factor the numerator. We need two numbers with a sum of 3 and a product of 2. The numbers 1 and 2 satisfy these conditions:
Now, look to see if there are any common factors that will cancel:
The in the numerator and denominator cancel, leaving .
First factor the numerator. We need two numbers with a sum of 3 and a product of 2. The numbers 1 and 2 satisfy these conditions:
Now, look to see if there are any common factors that will cancel:
The
Simplify.
Simplify.
Tap to see back →
a. Simplify the numerator and denominator separately by pulling out common factors.
b. Reduce if possible.
c. Factor the trinomial in the numerator.
d. Cancel common factors between the numerator and the denominator.
a. Simplify the numerator and denominator separately by pulling out common factors.
b. Reduce if possible.
c. Factor the trinomial in the numerator.
d. Cancel common factors between the numerator and the denominator.
Transform the following equation from standard into vertex form:
Transform the following equation from standard into vertex form:
Tap to see back →
To take this standard form equation and transform it into vertex form, we need to complete the square. That can be done as follows:
We will complete the square on . In this case, our in our soon-to-be is . We therefore want our , so .
Since we are adding on the right side (as we are completing the square inside the parentheses), we need to add on the left side as well. Our equation therefore becomes:
Our final answer is therefore
To take this standard form equation and transform it into vertex form, we need to complete the square. That can be done as follows:
We will complete the square on
Since we are adding
Our final answer is therefore
Evaluate the following expression:
Evaluate the following expression:
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When we multiply expressions with exponents, we need to keep in mind some rules:
Multiplied variables add exponents.
Divided variables subtract exponents.
Variables raised to a power multiply exponents.
Therefore, when we mulitiply the two fractions, we obtain:
Our final answer is therefore
When we multiply expressions with exponents, we need to keep in mind some rules:
Multiplied variables add exponents.
Divided variables subtract exponents.
Variables raised to a power multiply exponents.
Therefore, when we mulitiply the two fractions, we obtain:
Our final answer is therefore
Simplify this rational expression:
Simplify this rational expression:
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To see what can be simplified, factor the quadratic equations.
Cancel out like terms:
Combine terms:
To see what can be simplified, factor the quadratic equations.
Cancel out like terms:
Combine terms:
Simplify the rational expression by factoring:
Simplify the rational expression by factoring:
Tap to see back →
To simplify it is best to completely factor all polynomials:
Now cancel like terms:
Combine like terms:
To simplify it is best to completely factor all polynomials:
Now cancel like terms:
Combine like terms:
Factor and simplify this rational expression:
Factor and simplify this rational expression:
Tap to see back →
Completely factor all polynomials:
Cancel like terms:
Completely factor all polynomials:
Cancel like terms:
Factor .
Factor
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In the beginning, we can treat this as two separate problems, and factor the numerator and the denominator independently:
After we've factored them, we can put the factored equations back into the original problem:
From here, we can cancel the from the top and the bottom, leaving:
In the beginning, we can treat this as two separate problems, and factor the numerator and the denominator independently:
After we've factored them, we can put the factored equations back into the original problem:
From here, we can cancel the