Solve 2/5x+5-3/x^2-1=4/x-1

$$\frac { 2 } { 5 x + 5 } - \frac { 3 } { x ^ { 2 } - 1 } = \frac { 4 } { x - 1 }$$

Solve for x

$$x = -\frac{37}{18} = -2\frac{1}{18} \approx -2.055555556$$

Steps for Solving Linear Equation

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

$$\left(x-1\right)\times 2-5\times 3=\left(5x+5\right)\times 4$$

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

$$2x-2-5\times 3=\left(5x+5\right)\times 4$$

Multiply -5 and 3 to get -15.

$$2x-2-15=\left(5x+5\right)\times 4$$

Subtract 15 from -2 to get -17.

$$2x-17=\left(5x+5\right)\times 4$$

Use the distributive property to multiply 5x+5 by 4.

$$2x-17=20x+20$$

Subtract 20x from both sides.

$$2x-17-20x=20$$

Combine 2x and -20x to get -18x.

$$-18x-17=20$$

Add 17 to both sides.

$$-18x=20+17$$

Add 20 and 17 to get 37.

$$-18x=37$$

Divide both sides by -18.

$$x=\frac{37}{-18}$$

Fraction \frac{37}{-18} can be rewritten as -\frac{37}{18} by extracting the negative sign.

$$x=-\frac{37}{18}$$