Solve t+5/t-5=10

$$\frac { t + 5 } { t - 5 } = 10$$

Solve for t

$$t = \frac{55}{9} = 6\frac{1}{9} \approx 6.111111111$$

Steps for Solving Linear Equation

Variable t cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by t-5.

$$t+5=10\left(t-5\right)$$

Use the distributive property to multiply 10 by t-5.

$$t+5=10t-50$$

Subtract 10t from both sides.

$$t+5-10t=-50$$

Combine t and -10t to get -9t.

$$-9t+5=-50$$

Subtract 5 from both sides.

$$-9t=-50-5$$

Subtract 5 from -50 to get -55.

$$-9t=-55$$

Divide both sides by -9.

$$t=\frac{-55}{-9}$$

Fraction \frac{-55}{-9} can be simplified to \frac{55}{9} by removing the negative sign from both the numerator and the denominator.

$$t=\frac{55}{9}$$