Solve 2/x-5-7/x+2=-1/x^2-3x-10

$$\frac { 2 } { x - 5 } - \frac { 7 } { x + 2 } = \frac { - 1 } { x ^ { 2 } - 3 x - 10 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+2\right), the least common multiple of x-5,x+2,x^{2}-3x-10.

$$\left(x+2\right)\times 2-\left(x-5\right)\times 7=-1$$

Use the distributive property to multiply x+2 by 2.

$$2x+4-\left(x-5\right)\times 7=-1$$

Use the distributive property to multiply x-5 by 7.

$$2x+4-\left(7x-35\right)=-1$$

To find the opposite of 7x-35, find the opposite of each term.

$$2x+4-7x+35=-1$$

Combine 2x and -7x to get -5x.

$$-5x+4+35=-1$$

Add 4 and 35 to get 39.

$$-5x+39=-1$$

Subtract 39 from both sides.

$$-5x=-1-39$$

Subtract 39 from -1 to get -40.

$$-5x=-40$$

Divide both sides by -5.

$$x=\frac{-40}{-5}$$

Divide -40 by -5 to get 8.

$$x=8$$