Question

Which of the following is the simplified form of x minus 7 over 2 x minus 12 plus the fraction 6 over x squared minus 36

Answer 1

do u mean \[x - 7/2x - 12 + 6 / (x ^{2} - 36)\] ?

Answer 2

yes

Answer 3

\[\frac{x -7}{2x -12}+\frac{6}{x^2 - 36}\]

factorise the denominators

\[\frac{ x - 7}{2(x -6)} + \frac{ 6}{(x - 6)(x + 6)}\]

now you need to find the common denominator

Answer 4

is it x + 5/ 2(x + 6)?

Answer 5

the common denominator will be 2(x-6)(x+6). take LCM.

Answer 6

getting a common denominator can be done by the following calculation

\[\frac{(x -7)}{2(x -6)} \times \frac{(x +6)}{(x+6} + \frac{6}{(x -6)(x +6)} \times \frac{2}{2}\]

which gives

\[\frac{(x -7)(x +6)}{2(x-6)(x+6)} + \frac{ 6\times2}{2(x-6)(x+6)}\]

next you will need to expand the numerator, collect like terms and cancel any common factors

Answer 7

and yes you solution is correct