Solve -5t/t^2-36-7/t+6=1/t-6

$$\frac { - 5 t } { t ^ { 2 } - 36 } - \frac { 7 } { t + 6 } = \frac { 1 } { t - 6 }$$

Solve for t

$$t = \frac{36}{13} = 2\frac{10}{13} \approx 2.769230769$$

Steps for Solving Linear Equation

Variable t cannot be equal to any of the values -6,6 since division by zero is not defined. Multiply both sides of the equation by \left(t-6\right)\left(t+6\right), the least common multiple of t^{2}-36,t+6,t-6.

$$-5t-\left(t-6\right)\times 7=t+6$$

Use the distributive property to multiply t-6 by 7.

$$-5t-\left(7t-42\right)=t+6$$

To find the opposite of 7t-42, find the opposite of each term.

$$-5t-7t+42=t+6$$

Combine -5t and -7t to get -12t.

$$-12t+42=t+6$$

Subtract t from both sides.

$$-12t+42-t=6$$

Combine -12t and -t to get -13t.

$$-13t+42=6$$

Subtract 42 from both sides.

$$-13t=6-42$$

Subtract 42 from 6 to get -36.

$$-13t=-36$$

Divide both sides by -13.

$$t=\frac{-36}{-13}$$

Fraction \frac{-36}{-13} can be simplified to \frac{36}{13} by removing the negative sign from both the numerator and the denominator.

$$t=\frac{36}{13}$$