### All Algebra 1 Resources

## Example Questions

### Example Question #4 : Solving Rational Expressions

Simplify:

**Possible Answers:**

**Correct answer:**

Factor out from the numerator which gives us

Hence we get the following

which is equal to

### Example Question #1 : Factoring Rational Expressions

Simplify:

**Possible Answers:**

**Correct answer:**

If we factors the denominator we get

Hence the rational expression becomes equal to

which is equal to

### Example Question #1 : Understanding Rational Expressions

Which of the following fractions is NOT equivalent to ?

**Possible Answers:**

**Correct answer:**

We know that is equivalent to or .

By this property, there is no way to get from .

Therefore the correct answer is .

### Example Question #5 : Rational Expressions

Find the values of which will make the given rational expression undefined:

**Possible Answers:**

**Correct answer:**

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 : Solving Rational Expressions

Solve for .

**Possible Answers:**

,

,

,

,

**Correct answer:**

,

The two fractions on the left side of the equation need a common denominator. We can easily do find one by multiplying both the top and bottom of each fraction by the denominator of the other.

becomes .

becomes .

Now add the two fractions:

To solve, multiply both sides of the equation by , yielding

.

Multiply both sides by 3:

Move all terms to the same side:

This looks like a complicated equation to factor, but luckily, the only factors of 37 are 37 and 1, so we are left with

.

Our solutions are therefore

and

.

### Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Simplify the expression:

**Possible Answers:**

**Correct answer:**

First, factor out x from the numerator:

Notice that the resultant expression in the parentheses is quadratic. This expression can be further factored:

We can then cancel the (x-3) which appears in both the numerator and denominator:

Finally, distribute the x outside of the parentheses to reach our answer:

### Example Question #2 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Solve for .

**Possible Answers:**

None of the other answers.

**Correct answer:**

Multiply each side by

Distribute 2 to each term of the polynomial.

Divide the polynomial by 6.

Divide each side by 6.

Subtract the term from each side.

### Example Question #3 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Solve for .

**Possible Answers:**

**Correct answer:**

Multiply each side by

Distribute 3 to the terms in parentheses.

Subtract 6 from each side of the equation.

Divide each side by 3.

### Example Question #4 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Solve for .

**Possible Answers:**

**Correct answer:**

Multiply each side of the equation by

Distribute 5 to each term in parentheses.

Subtract 25 from each side of equation.

Divide each side of equation by 5.

Square root of each side of equation.

### Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

For all values , which of the following is equivalent to the expression above?

**Possible Answers:**

**Correct answer:**

First, factor the numerator. We need factors that multiply to and add to .

We can plug the factored terms into the original expression.

Note that appears in both the numerator and the denominator. This allows us to cancel the terms.

This is our final answer.

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