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Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator
Which of the following fractions is NOT equivalent to ?
We know that is equivalent to
or
.
By this property, there is no way to get from
.
Therefore the correct answer is .
Example Question #1 : Definition Of Rational Expression
Determine the domain of
All real numbers
Because the denominator cannot be zero, the domain is all other numbers except for 1, or
Example Question #3 : Rational Expressions
Simplify:
This problem is a lot simpler if we factor all the expressions involved before proceeding:
Next let's remember how we divide one fraction by another—by multiplying by the reciprocal:
In this form, we can see that a lot of terms are going to start canceling with each other. All that we're left with is just .
Example Question #4 : Rational Expressions
Which of the following is the best definition of a rational expression?
The rational expression is a ratio of two polynomials.
The denominator cannot be zero.
An example of a rational expression is:
The answer is:
Example Question #5 : Rational Expressions
Find the values of which will make the given rational expression undefined:
If or
, the denominator is 0, which makes the expression undefined.
This happens when x = 1 or when x = -2.
Therefore the correct answer is .
Example Question #6 : Rational Expressions
Simply the expression:
In order to simplify the expression , we need to ensure that both terms have the same denominator. In order to do so, find the Least Common Denominator (LCD) for both terms and simplify the expression accordingly:
Example Question #1 : Properties Of Fractions
Simplify the expression:
In order to simplify the expression , first note that the denominators in both terms share a factor:
Find the Least Common Denominator (LCD) of both terms:
Finally, combine like terms:
Example Question #8 : Rational Expressions
Simplify the expression:
1. Create a common denominator between the two fractions.
2. Simplify.
Example Question #9 : Rational Expressions
Find the values of which will make this rational expression undefined:
For a rational expression to be undefined, the denominator must be equal to .
1. Set the denominator equal to .
2. Set the factors equal to and solve for
.
and
Example Question #1 : Rational Expressions
Which value of makes the following expression undefined?
A rational expression is undefined when the denominator is zero.
The denominator is zero when .
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