Q:

who solves this question would be marked as brainliest​

Accepted Solution

A:
Answer: x = 1 [tex]\frac{3}{7}[/tex] or x = -2Step-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 = 0solving the resulting quadratic equation by factorization , we have(14x - 20)(x + 2 ) = 014x - 20 = 0  or x + 2 = 014x = 20       or x = -2x = 20/ 14      or x = -2 Therefore x = 10/7 or x = -2x = 1 [tex]\frac{3}{7}[/tex] or x = -2