Solve x+5/(2x-1)(x+1)-1/x+1=2/2x-1

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

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

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

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

To find the opposite of 2x-1, find the opposite of each term.

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

Combine x and -2x to get -x.

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

Add 5 and 1 to get 6.

$$-x+6=\left(x+1\right)\times 2$$

Use the distributive property to multiply x+1 by 2.

$$-x+6=2x+2$$

Subtract 2x from both sides.

$$-x+6-2x=2$$

Combine -x and -2x to get -3x.

$$-3x+6=2$$

Subtract 6 from both sides.

$$-3x=2-6$$

Subtract 6 from 2 to get -4.

$$-3x=-4$$

Divide both sides by -3.

$$x=\frac{-4}{-3}$$

Fraction \frac{-4}{-3} can be simplified to \frac{4}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{3}$$