Answer: x = 1 [tex]\frac{3}{7}[/tex] or x = -2
Step-by-step explanation:
The first step is to find the L.C.M of the L.H.S
[tex]\frac{9+7(2x-5)}{9(2x-5)}[/tex] = [tex]\frac{2}{x+5}[/tex]
⇒ [tex]\frac{9+14x-35}{9(2x-5)}[/tex] = [tex]\frac{2}{x+5}[/tex]
[tex]\frac{14x-26}{9(2x-5)}[/tex] = [tex]\frac{2}{x+5}[/tex]
cross multiplying , we have
(x+5)(14x - 26) = 18(2x-5)
Expanding, we have
[tex]14x^{2}[/tex] + 44x - 130 = 36x - 90
[tex]14x^{2}[/tex] + 44x - 130 - 36x + 90 = 0
[tex]14x^{2}[/tex] + 8x - 40 = 0
solving the resulting quadratic equation by factorization , we have
(14x - 20)(x + 2 ) = 0
14x - 20 = 0 or x + 2 = 0
14x = 20 or x = -2
x = 20/ 14 or x = -2
Therefore x = 10/7 or x = -2
x = 1 [tex]\frac{3}{7}[/tex] or x = -2
