Solve c+4/c+8=c+3/c+5

$$\frac { c + 4 } { c + 8 } = \frac { c + 3 } { c + 5 }$$

Solve for c

$$c=-2$$

Steps for Solving Linear Equation

Variable c cannot be equal to any of the values -8,-5 since division by zero is not defined. Multiply both sides of the equation by \left(c+5\right)\left(c+8\right), the least common multiple of c+8,c+5.

$$\left(c+5\right)\left(c+4\right)=\left(c+8\right)\left(c+3\right)$$

Use the distributive property to multiply c+5 by c+4 and combine like terms.

$$c^{2}+9c+20=\left(c+8\right)\left(c+3\right)$$

Use the distributive property to multiply c+8 by c+3 and combine like terms.

$$c^{2}+9c+20=c^{2}+11c+24$$

Subtract c^{2} from both sides.

$$c^{2}+9c+20-c^{2}=11c+24$$

Combine c^{2} and -c^{2} to get 0.

$$9c+20=11c+24$$

Subtract 11c from both sides.

$$9c+20-11c=24$$

Combine 9c and -11c to get -2c.

$$-2c+20=24$$

Subtract 20 from both sides.

$$-2c=24-20$$

Subtract 20 from 24 to get 4.

$$-2c=4$$

Divide both sides by -2.

$$c=\frac{4}{-2}$$

Divide 4 by -2 to get -2.

$$c=-2$$