Question

$2(x - 1 \div x + 3) - 7(x + 3 \div x - 1) = 5$
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Answer 1

Answer:

The solutions are -1 and -23/5

Step-by-step explanation:

$2(\frac{x-1}{x+3})-7(\frac{x+3}{x-1})=5$

$\frac{2(x-1)^2-7(x+3)^2}{(x+3)(x-1)}=5$

$2(x-1)^2-7(x+3)^2=5(x+3)(x-1)$

$2[x^2+1-2x]-7[x^2+9+6x=5[x^2+2x-3]$

$2x^2+2-4x-7x^2-63-42x=5x^2+10x-15$

$-5x^2-61-46x=5x^2+10x-15$

$-10x^2-56x-46=0$

$\implies\:5x^2+5x+23x+23=0$

$5x(x+1)+23(x+1)=0$

$(5x+23)(x+1)=0$

$\implies\:\boxed{x=-1,\frac{-23}{5}}$