# Algebra 1 : How to find the solution of a rational equation with a binomial denominator

## Example Questions

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

Simplify:

Explanation:

Factor out  from the numerator which gives us

Hence we get the following

which is equal to

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

Simplify:

Explanation:

If we factors the denominator we get

Hence the rational expression becomes equal to

which is equal to

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

Which of the following fractions is NOT equivalent to ?

Explanation:

We know that is equivalent to or .

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

Therefore the correct answer is .

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

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

Explanation:

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

Solve for .

Explanation:

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 .

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.

Explanation:

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.

### Example Question #5 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Simplify the expression:

Explanation:

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 #43 : Binomials

Solve for .

Explanation:

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 #6 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Solve for .

Explanation:

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

Solve for .

Explanation:

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.