Question

Simplify the expression

Answer 1

Given :-

`((1)/(c)+(1)/(d))/((c)/(d)-(d)/(c))`

...
`((c+d)/(cd) )/((c^(2)-d^(2))/(cd) )`

a² - b² = ( a + b ) ( a - b )

...
`((c+d)/(cd))/(((c+d)(c-d))/(cd))`

...
`(c+d)/(cd)*(cd)/((c+d)(c-d))`

...
`((c+d))/((c+d)(c-d))`

...
`(1)/(c-d)` Is the answer.

Hope my answer helps!!

Answer 2

1/(c - d)

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((1)/(c)+(1)/(d))/((c)/(d)-(d)/(c))=(d+c)/(c^2-d^2)\\\\=(d+c)/((c-d)(d+c))=(1)/(c-d)`