Question

Please help me and show working. I have a test very soon.

Answer 1

c = 3

Explanation:

Given

`(2)/(c-2)` -
`(3)/(c+2)` =
`(7)/(c^2-4)` ← factor the difference of squares

`(2)/(c-2)` -
`(3)/(c+2)` =
`(7)/((c-2)(c+2))`

Multiply through by (c - 2)(c + 2) to clear the fractions

2(c + 2) - 3(c - 2) = 7 ← distribute and simplify left side

2c + 4 - 3c + 6 = 7

- c + 10 = 7 ( subtract 10 from both sides )

- c = - 3 ( multiply both sides by - 1 )

c = 3