Precalculus Examples

$\frac{p + 3}{5 - 2 p} = t$

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$5 - 2 p, 1$

Step 1.2

Remove parentheses.

$5 - 2 p, 1$

Step 1.3

The LCM of one and any expression is the expression.

$5 - 2 p$

Step 2

Multiply each term in $\frac{p + 3}{5 - 2 p} = t$ by $5 - 2 p$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $\frac{p + 3}{5 - 2 p} = t$ by $5 - 2 p$ .

$\frac{p + 3}{5 - 2 p} (5 - 2 p) = t (5 - 2 p)$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $5 - 2 p$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{p + 3}{5 - 2 p} (5 - 2 p) = t (5 - 2 p)$

Step 2.2.1.2

Rewrite the expression.

$p + 3 = t (5 - 2 p)$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

$p + 3 = t \cdot 5 + t (- 2 p)$

Step 2.3.2

Reorder.

Tap for more steps...

Step 2.3.2.1

Move $5$ to the left of $t$ .

$p + 3 = 5 \cdot t + t (- 2 p)$

Step 2.3.2.2

Rewrite using the commutative property of multiplication.

$p + 3 = 5 t - 2 t p$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Add $2 t p$ to both sides of the equation.

$p + 3 + 2 t p = 5 t$

Step 3.2

Subtract $3$ from both sides of the equation.

$p + 2 t p = 5 t - 3$

Step 3.3

Factor $p$ out of $p + 2 t p$ .

Tap for more steps...

Step 3.3.1

Factor $p$ out of $p^{1}$ .

$p \cdot 1 + 2 t p = 5 t - 3$

Step 3.3.2

Factor $p$ out of $2 t p$ .

$p \cdot 1 + p (2 t) = 5 t - 3$

Step 3.3.3

Factor $p$ out of $p \cdot 1 + p (2 t)$ .

$p (1 + 2 t) = 5 t - 3$

Step 3.4

Divide each term in $p (1 + 2 t) = 5 t - 3$ by $1 + 2 t$ and simplify.

Tap for more steps...

Step 3.4.1

Divide each term in $p (1 + 2 t) = 5 t - 3$ by $1 + 2 t$ .

$\frac{p (1 + 2 t)}{1 + 2 t} = \frac{5 t}{1 + 2 t} + \frac{- 3}{1 + 2 t}$

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Cancel the common factor of $1 + 2 t$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor.

$\frac{p (1 + 2 t)}{1 + 2 t} = \frac{5 t}{1 + 2 t} + \frac{- 3}{1 + 2 t}$

Step 3.4.2.1.2

Divide $p$ by $1$ .

$p = \frac{5 t}{1 + 2 t} + \frac{- 3}{1 + 2 t}$

Step 3.4.3

Simplify the right side.

Tap for more steps...

Step 3.4.3.1

Combine the numerators over the common denominator.

$p = \frac{5 t - 3}{1 + 2 t}$