# How do you simplify (d+7)/(d^-49)?

Jul 3, 2015

I think you meant $\frac{d + 7}{{d}^{2} - 49}$

If so, the answer is $\frac{1}{d - 7}$ with exclusion $d \ne - 7$

#### Explanation:

$\frac{d + 7}{{d}^{2} - 49}$

$= \frac{d + 7}{{d}^{2} - {7}^{2}}$

$= \frac{d + 7}{\left(d - 7\right) \left(d + 7\right)}$

$= \frac{1}{d - 7}$

With exclusion $d \ne - 7$

using the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

with $a = d$ and $b = 7$