Question

Please can someone help asap ? thank you ! :)

Answer 1

`(x + 2)/(3x - 1)`

Explanation:

Things you should before solving this question :-

• a²- b² = (a + b)(a - b)

where a and b are any two variables.

SIMPLIFYING THE EXPRESSION

`\frac{ {x}^(2) - 9 }{3 {x}^(2) + 8x - 3} / (x - 3)/(x + 2) \\`

using the identity discussed above

`\frac{ (x + 3)(x - 3) }{3 {x}^(2) + 8x - 3} / (x - 3)/(x + 2)`

simplifying 3x² + 8x - 3

`\frac{ {x}^(2) - 9 }{3 {x}^(2) + 9x -x - 3} / (x - 3)/(x + 2)`

as 8x can be written as 9x - x

`\frac{ (x - 3)(x + 3) }{3 {x}(x + 3) - 1(x + 3)} / (x - 3)/(x + 2) \\ \frac{ (x - 3)(x + 3) }{(3 {x} - 1)(x + 3) } / (x - 3)/(x + 2)`

flipping the fraction that follows division sign and inserting multiply in place of divide

`\frac{ (x - 3)(x + 3) }{(3 {x} - 1)(x + 3) } * (x + 2)/(x - 3)`

canceling (x - 3) and (x + 3) as they're common in both denominator and numerator

`(x + 2)/(3x - 1)`