Vocabulary

Lesson

To simplify rational expressions, first we need to know what they are. They are fractions that have polynomials on both their numerators and denominators.

${\displaystyle {\frac {2x^{2}+8x+8}{6x-2}}}$

You just can simplify factors, not terms. That means you have to factorize the nominator and the denominator:

${\displaystyle {\frac {2x^{2}+8x+8}{6x-2}}}$

${\displaystyle ={\frac {2(x+2)^{2}}{2(3x-1)}}}$

Now, both are divisible by 2. So just divide them by 2, the result would be:

${\displaystyle ={\frac {(x+2)^{2}}{3x-1}}}$

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