Solve for t m=(t+1)/(t-3)

$m = \frac{t + 1}{t - 3}$

Step 1

Multiply the equation by $t - 3$ .

$(t - 3) (m) = (\frac{t + 1}{t - 3}) (t - 3)$

Step 2

Simplify the left side.

Apply the distributive property.

$t m - 3 m = (\frac{t + 1}{t - 3}) (t - 3)$

Step 3

Simplify the right side.

Cancel the common factor of $t - 3$ .

Cancel the common factor.

$t m - 3 m = \frac{t + 1}{t - 3} (t - 3)$

Rewrite the expression.

$t m - 3 m = t + 1$

Step 4

Solve for $t$ .

Subtract $t$ from both sides of the equation.

$t m - 3 m - t = 1$

Add $3 m$ to both sides of the equation.

$t m - t = 1 + 3 m$

Factor $t$ out of $t m - t$ .

Factor $t$ out of $t m$ .

$t (m) - t = 1 + 3 m$

Factor $t$ out of $- t$ .

$t (m) + t \cdot - 1 = 1 + 3 m$

Factor $t$ out of $t (m) + t \cdot - 1$ .

$t (m - 1) = 1 + 3 m$

Divide each term in $t (m - 1) = 1 + 3 m$ by $m - 1$ and simplify.

Divide each term in $t (m - 1) = 1 + 3 m$ by $m - 1$ .

$\frac{t (m - 1)}{m - 1} = \frac{1}{m - 1} + \frac{3 m}{m - 1}$

Simplify the left side.

Cancel the common factor of $m - 1$ .

Cancel the common factor.

$\frac{t (m - 1)}{m - 1} = \frac{1}{m - 1} + \frac{3 m}{m - 1}$

Divide $t$ by $1$ .

$t = \frac{1}{m - 1} + \frac{3 m}{m - 1}$

Simplify the right side.

Combine the numerators over the common denominator.

$t = \frac{1 + 3 m}{m - 1}$