Question

Solve for x
x²-3x-28/x²-49=3/17
x≠±7
[Hint: x²- 49=(x+7)(x-7)
Factorise the numerator.]

Answer 1

Answer:

$x=\frac{-47}{14}$

Step-by-step explanation:

Given : $\frac{x^2-3x-28}{x^2-49} =\frac{3}{17}$

Solution:

$\frac{x^2-3x-28}{x^2-7^2} =\frac{3}{17}$

Using property $a^2-b^2=(a+b)(a-b)$

$\frac{x^2-3x-28}{(x+7)(x-7)} =\frac{3}{17}$

$\frac{x^2-7x+4x-28}{(x+7)(x-7)} =\frac{3}{17}$

$\frac{x(x-7)+4(x-7)}{(x+7)(x-7)} =\frac{3}{17}$

$\frac{(x-7)(x+4)}{(x+7)(x-7)} =\frac{3}{17}$

$\frac{x+4}{x+7} =\frac{3}{17}$

$17(x+4)=3(x+7)$

$17x+68=3x+21$

$17x-3x=-68+21$

$14x=-47$

$x=\frac{-47}{14}$

Hence $x=\frac{-47}{14}$

Answer 2

Hope it will help you...