Solve 7x-8/1-5x=x-8/x+7

$$\frac { 7 x - 8 } { 1 - 5 x } = \frac { x - 8 } { x + 7 }$$

Solve for x

$$x=-2$$

$$x=2$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -7,\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-1\right)\left(x+7\right), the least common multiple of 1-5x,x+7.

$$-\left(7+x\right)\left(7x-8\right)=\left(5x-1\right)\left(x-8\right)$$

To find the opposite of 7+x, find the opposite of each term.

$$\left(-7-x\right)\left(7x-8\right)=\left(5x-1\right)\left(x-8\right)$$

Use the distributive property to multiply -7-x by 7x-8 and combine like terms.

$$-41x+56-7x^{2}=\left(5x-1\right)\left(x-8\right)$$

Use the distributive property to multiply 5x-1 by x-8 and combine like terms.

$$-41x+56-7x^{2}=5x^{2}-41x+8$$

Subtract 5x^{2} from both sides.

$$-41x+56-7x^{2}-5x^{2}=-41x+8$$

Combine -7x^{2} and -5x^{2} to get -12x^{2}.

$$-41x+56-12x^{2}=-41x+8$$

Add 41x to both sides.

$$-41x+56-12x^{2}+41x=8$$

Combine -41x and 41x to get 0.

$$56-12x^{2}=8$$

Subtract 56 from both sides.

$$-12x^{2}=8-56$$

Subtract 56 from 8 to get -48.

$$-12x^{2}=-48$$

Divide both sides by -12.

$$x^{2}=\frac{-48}{-12}$$

Divide -48 by -12 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -7,\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-1\right)\left(x+7\right), the least common multiple of 1-5x,x+7.

$$-\left(7+x\right)\left(7x-8\right)=\left(5x-1\right)\left(x-8\right)$$

To find the opposite of 7+x, find the opposite of each term.

$$\left(-7-x\right)\left(7x-8\right)=\left(5x-1\right)\left(x-8\right)$$

Use the distributive property to multiply -7-x by 7x-8 and combine like terms.

$$-41x+56-7x^{2}=\left(5x-1\right)\left(x-8\right)$$

Use the distributive property to multiply 5x-1 by x-8 and combine like terms.

$$-41x+56-7x^{2}=5x^{2}-41x+8$$

Subtract 5x^{2} from both sides.

$$-41x+56-7x^{2}-5x^{2}=-41x+8$$

Combine -7x^{2} and -5x^{2} to get -12x^{2}.

$$-41x+56-12x^{2}=-41x+8$$

Add 41x to both sides.

$$-41x+56-12x^{2}+41x=8$$

Combine -41x and 41x to get 0.

$$56-12x^{2}=8$$

Subtract 8 from both sides.

$$56-12x^{2}-8=0$$

Subtract 8 from 56 to get 48.

$$48-12x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-12x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -12 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 48}}{2\left(-12\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 48}}{2\left(-12\right)}$$

Multiply -4 times -12.

$$x=\frac{0±\sqrt{48\times 48}}{2\left(-12\right)}$$

Multiply 48 times 48.

$$x=\frac{0±\sqrt{2304}}{2\left(-12\right)}$$

Take the square root of 2304.

$$x=\frac{0±48}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{0±48}{-24}$$

Now solve the equation x=\frac{0±48}{-24} when ± is plus. Divide 48 by -24.

$$x=-2$$

Now solve the equation x=\frac{0±48}{-24} when ± is minus. Divide -48 by -24.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$