Question

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.a²-36/5a + 30Rational expression in lowest terms:Variable restrictions for the original expression: a

Answer 1

The expression is given to be:

$\frac{a^2-36}{5a+30}$

From the numerator, using the difference of two squares, we have:

$a^2-36=a^2-6^2=(a-6)(a+6)$

From the denominator, by factorization, we have:

$5a+30=5(a+6)$

Therefore, the expression becomes:

$\Rightarrow\frac{(a-6)(a+6)}{5(a+6)}$

Cancel out common terms in the denominator and numerator. The simplified expression will be:

$\Rightarrow\frac{a-6}{5}$

From the original expression, the variable restriction will be at:

$\begin{gathered} 5a+30=0 \\ Solving \\ 5a=-30 \\ a=-\frac{30}{5} \\ a=-6 \end{gathered}$

The restriction is:

$-6$