Question

Solve by factoring: from Quadratic equation

$4. \: \: \frac{2}{x + 1} - \frac{4}{2x - 7} = \frac{3}{2 - x}$
; x # - 1, 7/2 , 2

Standard:- 10

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Answer 1

The answer is (1/2), (5).


Hope it helps!

Answer 2

$\frac{2}{x+1} -\frac{4}{2x-7} = \frac{3}{2-x} \\ \\ \\ \implies \frac{2(2x-7)-4(x+1)}{(x+1)(2x-7)} = \frac{3}{2-x} \\ \\ \\ \implies \frac{4x-14-4x-4}{2x^2-7x+2x-7} = \frac{3}{2-x} \\ \\ \\ \implies \frac{-18}{2x^2-5x-7} = \frac{3}{2-x} \\ \\ \\ \implies \frac{-18}{3} (2-x) = 2x^2-5x-7 \\ \\ \\ \implies -6(2-x) = 2x^2-5x-7 \\ \\ \\ \implies -12+6x = 2x^2-5x-7 \\ \\ \\ \implies 2x^2-11x+5=0 \\ \\ \\ \implies 2x^2-10x-x+5=0 \\ \\ \\ \implies 2x(x-5) - 1(x-5)=0 \\ \\ \\ \implies (x-5)(2x-1) = 0$


$\implies x-5=0 \qquad OR \qquad 2x-1=0 \\ \\ \\ \implies \boxed{x=5} \qquad OR \qquad \boxed{x=\frac{1}{2}}$



Thus, the solutions of the equation are 5 and $\frac{\textbf{1}}{\textbf{2}}$