Solve 4/x+5=x-5/6

$$\frac{ 4 }{ x+5 } = \frac{ x-5 }{ 6 }$$

Solve for x

$$x=7$$

$$x=-7$$

Steps by Finding Square Root

Variable x cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by 6\left(x+5\right), the least common multiple of x+5,6.

$$6\times 4=\left(x+5\right)\left(x-5\right)$$

Multiply 6 and 4 to get 24.

$$24=\left(x+5\right)\left(x-5\right)$$

Consider \left(x+5\right)\left(x-5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

$$24=x^{2}-25$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-25=24$$

Add 25 to both sides.

$$x^{2}=24+25$$

Add 24 and 25 to get 49.

$$x^{2}=49$$

Take the square root of both sides of the equation.

$$x=7 x=-7$$

Steps Using the Quadratic Formula

Variable x cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by 6\left(x+5\right), the least common multiple of x+5,6.

$$6\times 4=\left(x+5\right)\left(x-5\right)$$

Multiply 6 and 4 to get 24.

$$24=\left(x+5\right)\left(x-5\right)$$

Consider \left(x+5\right)\left(x-5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

$$24=x^{2}-25$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-25=24$$

Subtract 24 from both sides.

$$x^{2}-25-24=0$$

Subtract 24 from -25 to get -49.

$$x^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$

Multiply -4 times -49.

$$x=\frac{0±\sqrt{196}}{2}$$

Take the square root of 196.

$$x=\frac{0±14}{2}$$

Now solve the equation x=\frac{0±14}{2} when ± is plus. Divide 14 by 2.

$$x=7$$

Now solve the equation x=\frac{0±14}{2} when ± is minus. Divide -14 by 2.

$$x=-7$$

The equation is now solved.

$$x=7 x=-7$$