Question

1/2x-3+1/x-5=10/9 solve x

Answer 1

cheers
Here is the answer for u r query

Answer 2

Answer:

$x =6\: Or\: \frac{37}{20}\:$

Step-by-step explanation:

$Given \: \frac{1}{2x-3}+\frac{1}{x-5}=\frac{10}{9}$

$\implies \frac{x-5+2x-3}{(2x-3)(x-5)}=\frac{10}{9}$

$\implies \frac{3x-8}{2x^{2}-10x-3x+15}=\frac{10}{9}$

$\implies \frac{3x-8}{2x^{2}-13x+15}=\frac{10}{9}$

$\implies 9(3x-8)=10(2x^{2}-13x+15)$

$\implies 27x-72 = 20x^{2}-130x+150$

$\implies 0=20x^{2}-130x-27x+150+72$

$\implies 20x^{2}-157x+222=0$

Compare above equation with ax²+bx+c=0, we get

a = 20, b = -157, c = 222

Discreminant (D)= b²-4ac

= (157)²-4×20×222

= 24649 - 17760

= 6889

By Quadratic Formula:

$x = \frac{-b±\sqrt{D}}{2a}$

$\implies x = \frac{-(-157)±\sqrt{6889}}{2\times 20}$

$=\frac{157±83}{40}$

$=\frac{157+83}{40}\: Or\: \frac{157-83}{40}\:$

$=\frac{240}{40}\: Or\: \frac{74}{40}\:$

$=6\: Or\: \frac{37}{20}\:$

Therefore,

$x =6\: Or\: \frac{37}{20}\:$

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