Question

simplify the expression below and state the value of m for which the simplified expression is not defined 2m² + m - 15/ m² - 9​

Answer 1

Answer:

• The simplified expression is: $\frac{2m-5}{m-3}$

• The simplified expression is undefined for m=3

Explanation:

The given expression is:

$\frac{2m^2+m-15}{m^2-9}$

The numerator can be siplified by using factorization and denominator will be simplified using the formula

$a^2-b^2 = (a+b)(a-b)$

So,

$= \frac{2m^2+6m-5m-15}{(m)^2-(3)^2}\\=\frac{2m(m+3)-5(m+3)}{(m-3)(m+3)}\\=\frac{(2m-5)(m+3)}{(m-3)(m+3)}\\=\frac{2m-5}{m-3}$

A fraction is undefined when the denominator is zero. In order to find the value of m on which the simplified fraction will be undefined we will put denominator equal to zero.

So,

$m-3 = 0 => m = 3$

Hence,

• The simplified expression is: $\frac{2m-5}{m-3}$

• The simplified expression is undefined for m=3