Answer
$\dfrac{70}{m^{2}-100}+\dfrac{7}{2(m+10)}=\dfrac{7}{2(m-10)}$
Work Step by Step
$\dfrac{70}{m^{2}-100}+\dfrac{7}{2(m+10)}$
Factor the denominator of the first fraction:
$\dfrac{70}{m^{2}-100}+\dfrac{7}{2(m+10)}=\dfrac{70}{(m-10)(m+10)}+\dfrac{7}{2(m+10)}=...$
Evaluate the sum of the two rational expressions and simplify:
$...=\dfrac{70(2)+7(m-10)}{2(m+10)(m-10)}=\dfrac{140+7m-70}{2(m+10)(m-10)}=...$
$...=\dfrac{7m+70}{2(m+10)(m-10)}=...$
Take out common factor $7$ from the numerator to provide a more simplified answer:
$...=\dfrac{7(m+10)}{2(m+10)(m-10)}=\dfrac{7}{2(m-10)}$
