Question

x+1/x-1+x-2/x+2=4-2x+3/x-2

Answer 1

Answer:

x = $\frac{6}{5}\:Or \:x = -5$

Step-by-step explanation:

$Given \: \frac{x+1}{x-2}+\frac{x-2}{x+2}\\=4-\frac{2x+3}{x-2}$

$\implies \frac{x-2}{x+2}+\frac{2x+3}{x-2}\\=4-\frac{x+1}{x-1}$

$\implies \frac{(x-2)^{2}+(x+2)(2x+3)}{(x+2)(x-2)}\\=\frac{4(x-1)-(x+1)}{x-1}$

$\implies \frac{x^{2}-4x+4+2x^{2}+3x+4x+6}{x^{2}-2^{2}}\\=\frac{4x-4-x-1}{x-1}$

$\implies \frac{3x^{2}+3x+10}{x^{2}-4}\\=\frac{3x-5}{x-1}$

$\implies (x-1)(3x^{2}+3x+10)\\=(x^{2}-4)(3x-5)$

$\implies (3x^{3}+3x^{2}+10x-3x^{2}-3x-10)\\=(3x^{3}-5x^{2}-12x+20)$

$\implies (3x^{3}+7x-10)-(3x^{3}-5x^{2}-12x+20)=0$

$\implies (3x^{3}+7x-10-3x^{3}+5x^{2}+12x-20)=0$

$\implies 5x^{2}+19x-30=0$

Compare above equation with

ax²+bx+c=0, we get

a = 5, b = 19, c = -30

Discreminant (D)=b²-4ac

= (19)²-4×19×(-30)

= 361+600

= 961

By Quadratic Formula:

x = [-b±√D]/(2a)

= $\frac{-19±\sqrt{961}}{2\times 5}$

=$\frac{-19±31}{10}$

Now,

x= $\frac{-19+31}{10}$

Or x =$\frac{-19-31}{10}$

x = $\frac{12}{10}\: Or\: x =\frac{-50}{10}$

x = $\frac{6}{5}\: Or \:x =-5$

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Answer 2

Answer:

Refer to Attachment

Step-by-step explanation:

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