Solve x^2-(x+5)(x-5)/x-5=3/7

$$\frac { x ^ { 2 } - ( x + 5 ) ( x - 5 ) } { x - 5 } = \frac { 3 } { 7 }$$

Solve for x

$$x = \frac{190}{3} = 63\frac{1}{3} \approx 63.333333333$$

Steps for Solving Linear Equation

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

$$7\left(x^{2}-\left(x+5\right)\left(x-5\right)\right)=3\left(x-5\right)$$

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.

$$7\left(x^{2}-\left(x^{2}-25\right)\right)=3\left(x-5\right)$$

To find the opposite of x^{2}-25, find the opposite of each term.

$$7\left(x^{2}-x^{2}+25\right)=3\left(x-5\right)$$

Combine x^{2} and -x^{2} to get 0.

$$7\times 25=3\left(x-5\right)$$

Multiply 7 and 25 to get 175.

$$175=3\left(x-5\right)$$

Use the distributive property to multiply 3 by x-5.

$$175=3x-15$$

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

$$3x-15=175$$

Add 15 to both sides.

$$3x=175+15$$

Add 175 and 15 to get 190.

$$3x=190$$

Divide both sides by 3.

$$x=\frac{190}{3}$$