Solve 1/5x+20-1/x^2-16=3/x-4

$$\frac { 1 } { 5 x + 20 } - \frac { 1 } { x ^ { 2 } - 16 } = \frac { 3 } { x - 4 }$$

Solve for x

$$x = -\frac{69}{14} = -4\frac{13}{14} \approx -4.928571429$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,4 since division by zero is not defined. Multiply both sides of the equation by 5\left(x-4\right)\left(x+4\right), the least common multiple of 5x+20,x^{2}-16,x-4.

$$x-4-5=\left(5x+20\right)\times 3$$

Subtract 5 from -4 to get -9.

$$x-9=\left(5x+20\right)\times 3$$

Use the distributive property to multiply 5x+20 by 3.

$$x-9=15x+60$$

Subtract 15x from both sides.

$$x-9-15x=60$$

Combine x and -15x to get -14x.

$$-14x-9=60$$

Add 9 to both sides.

$$-14x=60+9$$

Add 60 and 9 to get 69.

$$-14x=69$$

Divide both sides by -14.

$$x=\frac{69}{-14}$$

Fraction \frac{69}{-14} can be rewritten as -\frac{69}{14} by extracting the negative sign.

$$x=-\frac{69}{14}$$