Question

2x+5/2 -5x/x-1 =x pls help no spam or i report

Answer 1

Solution:-

$\sf \to \: \dfrac{2x + 5}{2} - \dfrac{5x}{x - 1} = x$

Taking lcm

$\sf \to \: \dfrac{(2x + 5)(x - 1) - 5x \times 2}{2(x - 1)} = x$

$\sf \to \dfrac{2 {x}^{2} - 2x + 5x - 5 - 10x }{2x - 2} = x$

$\sf \to \: 2 {x}^{2} - 7x - 5 = 2 {x}^{2} - 2x$

$\sf \to \: - 7x - 5 = - 2x$

$\sf \to \: - 7x + 2x = 5$

$\sf \to \: - 5x = 5$

$\sf \to \: x = - 1$

Now check our answer

$\sf \to \: \dfrac{2x + 5}{2} - \dfrac{5x}{x - 1} = x$

$\sf \to \: \dfrac{2 \times - 1 + 5}{2} - \dfrac{5 \times - 1}{ - 1- 1} = - 1$

$\sf \to \: \dfrac{ - 2 + 5}{2} - \dfrac{5}{2} = - 1$

$\sf \to \: \dfrac{ 3}{2} - \dfrac{5}{2} = - 1$

$\sf \to \: \dfrac{ - 2}{2} = - 1$

$\sf \to \: - 1 = - 1$

Hence proved