Question

Simplify the expression

Answer 1

Given :-

$\frac{\frac{1}{c}+\frac{1}{d}}{\frac{c}{d}-\frac{d}{c}}$

... $\frac{\frac{c+d}{cd} }{\frac{c^{2}-d^{2}}{cd} }$

a² - b² = ( a + b ) ( a - b )

... $\frac{\frac{c+d}{cd}}{\frac{(c+d)(c-d)}{cd}}$

... $\frac{c+d}{cd}*\frac{cd}{(c+d)(c-d)}$

... $\frac{(c+d)}{(c+d)(c-d)}$

... $\frac{1}{c-d}$ Is the answer.

Hope my answer helps!!

Answer 2

Answer:

1/(c - d)

Step-by-step explanation:

Multiply numerator and denominator by cd, then factor the denominator and cancel the common factor. (The result is restricted to c+d ≠ 0.)

$\displaystyle\frac{\frac{1}{c}+\frac{1}{d}}{\frac{c}{d}-\frac{d}{c}}=\frac{d+c}{c^2-d^2}\\\\=\frac{d+c}{(c-d)(d+c)}=\frac{1}{c-d}$