Solve (2x + 3)/(2x - 5) = (x + 1)/(x - 1); 5v+11112v\

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Question

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

Solve for x

$x=-\frac{1}{2}=-0.5$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to any of the values $1,\frac{5}{2}$ since division by zero is not defined. Multiply both sides of the equation by $\left(x-1\right)\left(2x-5\right)$, the least common multiple of $2x-5,x-1$.

$$\left(x-1\right)\left(2x+3\right)=\left(2x-5\right)\left(x+1\right)$$

Use the distributive property to multiply $x-1$ by $2x+3$ and combine like terms.

$$2x^{2}+x-3=\left(2x-5\right)\left(x+1\right)$$

Use the distributive property to multiply $2x-5$ by $x+1$ and combine like terms.

$$2x^{2}+x-3=2x^{2}-3x-5$$

Subtract $2x^{2}$ from both sides.

$$2x^{2}+x-3-2x^{2}=-3x-5$$

Combine $2x^{2}$ and $-2x^{2}$ to get $0$.

$$x-3=-3x-5$$

Add $3x$ to both sides.

$$x-3+3x=-5$$

Combine $x$ and $3x$ to get $4x$.

$$4x-3=-5$$

Add $3$ to both sides.

$$4x=-5+3$$

Add $-5$ and $3$ to get $-2$.

$$4x=-2$$

Divide both sides by $4$.

$$x=\frac{-2}{4}$$

Reduce the fraction $\frac{-2}{4}$ to lowest terms by extracting and canceling out $2$.

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

Show Solution