Solve 4s/s^2-100+6/s+10=1/s-10

$$\frac { 4 s } { s ^ { 2 } - 100 } + \frac { 6 } { s + 10 } = \frac { 1 } { s - 10 }$$

Solve for s

$$s = \frac{70}{9} = 7\frac{7}{9} \approx 7.777777778$$

Steps for Solving Linear Equation

Variable s cannot be equal to any of the values -10,10 since division by zero is not defined. Multiply both sides of the equation by \left(s-10\right)\left(s+10\right), the least common multiple of s^{2}-100,s+10,s-10.

$$4s+\left(s-10\right)\times 6=s+10$$

Use the distributive property to multiply s-10 by 6.

$$4s+6s-60=s+10$$

Combine 4s and 6s to get 10s.

$$10s-60=s+10$$

Subtract s from both sides.

$$10s-60-s=10$$

Combine 10s and -s to get 9s.

$$9s-60=10$$

Add 60 to both sides.

$$9s=10+60$$

Add 10 and 60 to get 70.

$$9s=70$$

Divide both sides by 9.

$$s=\frac{70}{9}$$