Question

With full explanation from the internet like before 1/(x-5)+3/(x+2)=4

Answer 1

Solution :

$x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2}$

Step-by-step explanation:

$\frac{1}{(x - 5)} + \frac{3}{(x - 2)} - 4$

1. Multiply by LCM

$x = 2 + 3( x - 5) = 4 - (x - 5)(x + 2)$

2. Solve

$x = 2 + 3(x - 5) = 4 (x - 5)(x + 2)$

$x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2}$

3.Verify Solutions

Find undefined (singularity) points :

x=5,x=–2

$x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2}$

Answer 2

$\\ \rm\Rrightarrow \dfrac{1}{x-5}+\dfrac{3}{x+2}=4$

$\\ \rm\Rrightarrow \dfrac{x+2+3x-15}{(x-5)(x+2)}=4$

$\\ \rm\Rrightarrow 4x-13=4(x-5)(x+2)$

$\\ \rm\Rrightarrow 4x-13=4(x(x+2)-5(x+2))$

$\\ \rm\Rrightarrow 4x-13=4(x^2+2x-5x-10)$

$\\ \rm\Rrightarrow 4x-13=4(x^2-3x-10)$

$\\ \rm\Rrightarrow 4x-13=4x^2-12x-40$

$\\ \rm\Rrightarrow 4x^2-16x-53=0$

On solving we get

$\\ \rm\Rrightarrow x=2\pm\dfrac{69}{2}$