Question

How do I simplify rational expressions in algebra 2

Answer 1

Given:

The expression is given as,

$\frac{x^3-7x+12}{9-x^2}$

The objective is to simplify the expression,

Explanation:

Rearrange the given expression as,

$\frac{x^3+0x^2-7x+12}{-x^2+9}$

Now, divide the polynomials using long division method.

To find the quotient divide only the first term of the dividend and the first term of the divisor.

$\frac{x^3}{-x^2}=-x$

To perform division:

Now, the division can be calculated as,

Thus, the result can be written as,

$-x+\frac{2x+12}{9-x^2}$

Hence, the simplified expression is obtained.