Solve {l}{2/x+3+2/x-3=20/x^2-9}{y=4}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{2}{x + 3} + \frac{2}{x - 3} = \frac{20}{x ^ {2} - 9} }\\ { y = 4 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=4$$

Solution Steps

Consider the first equation. Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right), the least common multiple of x+3,x-3,x^{2}-9.

$$\left(x-3\right)\times 2+\left(x+3\right)\times 2=20$$

Use the distributive property to multiply x-3 by 2.

$$2x-6+\left(x+3\right)\times 2=20$$

Use the distributive property to multiply x+3 by 2.

$$2x-6+2x+6=20$$

Combine 2x and 2x to get 4x.

$$4x-6+6=20$$

Add -6 and 6 to get 0.

$$4x=20$$

Divide both sides by 4.

$$x=\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$x=5$$

The system is now solved.

$$x=5 y=4 z=4$$