Question

2x+1/2x-3=2x-3/2x-1.pls solve​

Answer 1

Answer:

x = 5/6

Step-by-step explanation:

by cross multiplying we get,

(2x-1)(2x+1) = (2x-3)(2x-3)

→ 4x²-1 = (2x-3)² …(a+b)(a-b) = a²-b²

→ 4x²-1 = 4x²-2(2x)(3)+9 (a-b)² =a²-2ab

+b²

→ 4x²-1 = 4x²-12x+9

→ 4x²-4x²+12x = 9+1

→ 12x = 10

→ x = 10/12

→ x = 5/6

Answer 2

Answer:

The value of x is $\displaystyle{\sf\:\dfrac{5}{6}}$

Step-by-step-explanation:

The given equation is

$\displaystyle{\sf\:\dfrac{(\:2x\:+\:1\:)}{(\:2x\:-\:3\:)}\:=\:\dfrac{(\:2x\:-\:3\:)}{(\:2x\:-\:1\:)}}$

We have to find the value of x.

Now,

$\displaystyle{\sf\:\dfrac{(\:2x\:+\:1\:)}{(\:2x\:-\:3\:)}\:=\:\dfrac{(\:2x\:-\:3\:)}{(\:2x\:-\:1\:)}}$

$\displaystyle{\implies\sf\:(\:2x\:+\:1\:)\:\times\:(\:2x\:-\:1\:)\:=\:(\:2x\:-\:3\:)\:\times\:(\:2x\:-\:3\:)}$

$\displaystyle{\implies\sf\:2x\:\times\:(\:2x\:-\:1\:)\:+\:1\:\times\:(\:2x\:-\:1\:)\:=\:(\:2x\:-\:3\:)^2}$

$\displaystyle\implies\sf\:4x^2\:-\:\cancel{2x}\:+\:\cancel{2x}\:-\:1\:=\:(\:2x\:)^2\:-\:2\:\times\:2x\:\times\:3\:+\:(\:3\:)^2\:\:\:-\:-\:-\:[\:\because\:(\:a\:-\:b\:)^2\:=\:a^2\:-\:2ab\:+\:b^2\:]$

$\displaystyle{\implies\sf\:\cancel{4x^2}\:-\:1\:=\:\cancel{4x^2}\:-\:4x\:\times\:3\:+\:9}$

$\displaystyle{\implies\sf\:-\:1\:=\:-\:12x\:+\:9}$

$\displaystyle{\implies\sf\:-\:12x\:+\:9\:=\:-\:1}$

$\displaystyle{\implies\sf\:-\:12x\:=\:-\:1\:-\:9}$

$\displaystyle{\implies\sf\:\cancel{-}\:12x\:=\:\cancel{-}\:10}$

$\displaystyle{\implies\sf\:12x\:=\:10}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{10}{12}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:\dfrac{5}{6}}}}}$