Question

1/2x-3 +1/x-5 =1 solve for x

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$x=\frac{8+3\sqrt{2}}{2}$

Or

$x=\frac{8-3\sqrt{2}}{2}$

Explanation:

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

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

$\implies \frac{3x-8}{2x^{2}-10x-3x+15}=1$

$\implies \frac{3x-8}{2x^{2}-13x+15}=1$

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

$\implies 0= 2x^{2}-13x+15-3x+8=0$

$\implies 2x^{2}-16x+23=0$

Now ,

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

a = 2 , b = -16, c = 23

Discreminant (D) =b²-4ac

= (-16)²- 4×2×23

= 256 - 184

= 72

/* By Quadratic Formula */

$\boxed {x = \frac{-b±\sqrt{D}}{2a}}$

$x =\frac{-(-16)±\sqrt{72}}{2×2}$

= $\frac{16±6\sqrt{2}}{4}$

= $\frac{2(8±3\sqrt{2}}{4}$

= $\frac{8±3\sqrt{2}}{2}$

Therefore,

$x=\frac{8+3\sqrt{2}}{2}$

Or

$x=\frac{8-3\sqrt{2}}{2}$

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