Question

Solve: 2x+5/2-5x/x-1=x

Answer 1

Step-by-step explanation:

To solve

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

Take LCM in LHS

$\frac{2x.2(x - 1) + 5(x - 1) - 5x.2}{2(x - 1)} = x \\ \\ \frac{4x(x - 1) + 5(x - 1) - 10x}{2(x - 1)} = x$

on cross multiplication

$4 {x}^{2} - 4x + 5x - 5 - 10x = 2x(x - 1) \\ \\ 4 {x}^{2} - 9x - 5 = 2 {x}^{2} - 2x \\ \\ 4 {x}^{2} - 2 {x}^{2} - 9x + 2x - 5 = 0 \\ \\ 2 {x}^{2} - 7x - 5 = 0$

It cannot factorise further,if it is +5 then factors would be possible.

please check the question again .

Hope it helps you.

Answer 2

i think, you have written (2x + 5)/2 - 5x/(x - 1) = x

⇒(2x + 5)/2 - 5x/(x - 1) = x

⇒x + 5/2 - 5x/(x - 1) = x

⇒5/2 - 5x/(x - 1) = 0

⇒[5(x - 1) - 5x(2)] = 0

⇒[5x - 5 - 10x ] = 0

⇒(-5 - 5x) = 0

⇒-5(x + 1)= 0

⇒x = -1

hence, answer should be -1.

now if your question is 2x + 5/2 - 5x/(x - 1) = x

⇒x + 5/2 - 5x/(x - 1) = 0

⇒(x² - x - 5x)/(x - 1) + 5/2 = 0

⇒(x² - 6x)/(x - 1) = -5/2

⇒2x² - 12x = -5x + 5

⇒2x² - 7x - 5 = 0

⇒x = {7 ± √(49 + 40)}/4

⇒x = {7 ± √89}/4