Question

How do you simplify `\frac { 3- \frac { 7} { x + 7} } { \frac { 5} { x + 7} - 2}`?

Answer 1

`color(brown)( -(3x + 14) / (2x + 9)`

Explanation:

Numerator `= 3 - (7/(x+7))`

Taking L C M as (x + 7),

`=> (3(x+7) - 7) / (x+7) = (3x + 21 - 7) / (x+7) = (3x + 14) / (x + 7)`

Similarly Denominator `= ((5/(x+7)) - 2)`

`=> = (5 - 2x - 14)/(x + 7) = -(2x + 9) / (x + 7)`

`(Nr) / (Dr) = ( (3x + 14) / cancel(x + 7)) / (-(2x + 9) / cancel(x + 7))`

`=> = (3x + 14) / -(2x + 9) = -(3x + 14) / (2x + 9)`