Question

Simplify and state the restrictions.

Answer 1

Answer:

Simplified expression: $\frac{ -20m - 26}{(2m+1)(2m-5)(2m+5)}$

Restrictions: $m \neq -0.5, m \neq 2.5, m \neq -2.5$

Step-by-step explanation:

The expression is:

$\frac{2m-1}{4m^2-25} - \frac{2m+5}{4m^2-8m-5}$

We can simplify the denominator of the first fraction:

$\frac{2m-1}{(2m+5)(2m-5)} - \frac{2m+5}{4m^2-8m-5}$

Then we can simplify the denominator of the second fraction:

$\frac{2m-1}{(2m+5)(2m-5)} - \frac{2m+5}{(2m+1)(2m-5)}$

The least common multiple of the denominators is $(2m+1)(2m-5)(2m+5)$, therefore we have:

$\frac{(2m-1)(2m+1)}{(2m+1)(2m-5)(2m+5)} - \frac{(2m+5)^2}{(2m+1)(2m-5)(2m+5)}$

$\frac{4m^2-1}{(2m+1)(2m-5)(2m+5)} - \frac{4m^2+20m+25}{(2m+1)(2m-5)(2m+5)}$

$\frac{4m^2-1 - 4m^2 - 20m - 25}{(2m+1)(2m-5)(2m+5)}$

$\frac{ -20m - 26}{(2m+1)(2m-5)(2m+5)}$

The simplified expression is:

$\frac{ -20m - 26}{(2m+1)(2m-5)(2m+5)}$

The restrictions are the values of m that makes the denominator zero, so we calculate them using a 'not equal' sign:

$(2m+1) \neq 0 \rightarrow m \neq -0.5$

$(2m-5) \neq 0 \rightarrow m \neq 2.5$

$(2m+5) \neq 0 \rightarrow m \neq -2.5$