Solve t+7/t-9=t-3/t+1

$$\frac { t + 7 } { t - 9 } = \frac { t - 3 } { t + 1 }$$

Solve for t

$$t=1$$

Steps for Solving Linear Equation

Variable t cannot be equal to any of the values -1,9 since division by zero is not defined. Multiply both sides of the equation by \left(t-9\right)\left(t+1\right), the least common multiple of t-9,t+1.

$$\left(t+1\right)\left(t+7\right)=\left(t-9\right)\left(t-3\right)$$

Use the distributive property to multiply t+1 by t+7 and combine like terms.

$$t^{2}+8t+7=\left(t-9\right)\left(t-3\right)$$

Use the distributive property to multiply t-9 by t-3 and combine like terms.

$$t^{2}+8t+7=t^{2}-12t+27$$

Subtract t^{2} from both sides.

$$t^{2}+8t+7-t^{2}=-12t+27$$

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

$$8t+7=-12t+27$$

Add 12t to both sides.

$$8t+7+12t=27$$

Combine 8t and 12t to get 20t.

$$20t+7=27$$

Subtract 7 from both sides.

$$20t=27-7$$

Subtract 7 from 27 to get 20.

$$20t=20$$

Divide both sides by 20.

$$t=\frac{20}{20}$$

Divide 20 by 20 to get 1.

$$t=1$$