Solve 3/x^2-4-5/x^2+7x+10=0

$$\frac{ 3 }{ { x }^{ 2 } -4 } - \frac{ 5 }{ { x }^{ 2 } +7x+10 } =0$$

Solve for x

$$x = \frac{25}{2} = 12\frac{1}{2} = 12.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,-2,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+2\right)\left(x+5\right), the least common multiple of x^{2}-4,x^{2}+7x+10.

$$\left(x+5\right)\times 3-\left(x-2\right)\times 5=0$$

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

$$3x+15-\left(x-2\right)\times 5=0$$

Use the distributive property to multiply x-2 by 5.

$$3x+15-\left(5x-10\right)=0$$

To find the opposite of 5x-10, find the opposite of each term.

$$3x+15-5x+10=0$$

Combine 3x and -5x to get -2x.

$$-2x+15+10=0$$

Add 15 and 10 to get 25.

$$-2x+25=0$$

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

$$-2x=-25$$

Divide both sides by -2.

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

Fraction \frac{-25}{-2} can be simplified to \frac{25}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{25}{2}$$