Solve x/x+1-25/12+x/x-1=0

$$\frac { x } { x + 1 } - \frac { 25 } { 12 } + \frac { x } { x - 1 } = 0$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

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 12\left(x-1\right)\left(x+1\right), the least common multiple of x+1,12,x-1.

$$\left(12x-12\right)x+12\left(x-1\right)\left(x+1\right)\left(-\frac{25}{12}\right)+\left(12x+12\right)x=0$$

Use the distributive property to multiply 12x-12 by x.

$$12x^{2}-12x+12\left(x-1\right)\left(x+1\right)\left(-\frac{25}{12}\right)+\left(12x+12\right)x=0$$

Multiply 12 and -\frac{25}{12} to get -25.

$$12x^{2}-12x-25\left(x-1\right)\left(x+1\right)+\left(12x+12\right)x=0$$

Use the distributive property to multiply -25 by x-1.

$$12x^{2}-12x+\left(-25x+25\right)\left(x+1\right)+\left(12x+12\right)x=0$$

Use the distributive property to multiply -25x+25 by x+1 and combine like terms.

$$12x^{2}-12x-25x^{2}+25+\left(12x+12\right)x=0$$

Combine 12x^{2} and -25x^{2} to get -13x^{2}.

$$-13x^{2}-12x+25+\left(12x+12\right)x=0$$

Use the distributive property to multiply 12x+12 by x.

$$-13x^{2}-12x+25+12x^{2}+12x=0$$

Combine -13x^{2} and 12x^{2} to get -x^{2}.

$$-x^{2}-12x+25+12x=0$$

Combine -12x and 12x to get 0.

$$-x^{2}+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-25$$

Divide both sides by -1.

$$x^{2}=\frac{-25}{-1}$$

Fraction \frac{-25}{-1} can be simplified to 25 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

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 12\left(x-1\right)\left(x+1\right), the least common multiple of x+1,12,x-1.

$$\left(12x-12\right)x+12\left(x-1\right)\left(x+1\right)\left(-\frac{25}{12}\right)+\left(12x+12\right)x=0$$

Use the distributive property to multiply 12x-12 by x.

$$12x^{2}-12x+12\left(x-1\right)\left(x+1\right)\left(-\frac{25}{12}\right)+\left(12x+12\right)x=0$$

Multiply 12 and -\frac{25}{12} to get -25.

$$12x^{2}-12x-25\left(x-1\right)\left(x+1\right)+\left(12x+12\right)x=0$$

Use the distributive property to multiply -25 by x-1.

$$12x^{2}-12x+\left(-25x+25\right)\left(x+1\right)+\left(12x+12\right)x=0$$

Use the distributive property to multiply -25x+25 by x+1 and combine like terms.

$$12x^{2}-12x-25x^{2}+25+\left(12x+12\right)x=0$$

Combine 12x^{2} and -25x^{2} to get -13x^{2}.

$$-13x^{2}-12x+25+\left(12x+12\right)x=0$$

Use the distributive property to multiply 12x+12 by x.

$$-13x^{2}-12x+25+12x^{2}+12x=0$$

Combine -13x^{2} and 12x^{2} to get -x^{2}.

$$-x^{2}-12x+25+12x=0$$

Combine -12x and 12x to get 0.

$$-x^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 25}}{2\left(-1\right)}$$

Multiply 4 times 25.

$$x=\frac{0±\sqrt{100}}{2\left(-1\right)}$$

Take the square root of 100.

$$x=\frac{0±10}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±10}{-2}$$

Now solve the equation x=\frac{0±10}{-2} when ± is plus. Divide 10 by -2.

$$x=-5$$

Now solve the equation x=\frac{0±10}{-2} when ± is minus. Divide -10 by -2.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$