Precalculus Examples

$x = \frac{5}{t + 5}$ , $y = t + 5$

Step 1

Set up the parametric equation for $x (t)$ to solve the equation for $t$ .

$x = \frac{5}{t + 5}$

Step 2

Rewrite the equation as $\frac{5}{t + 5} = x$ .

$\frac{5}{t + 5} = x$

Step 3

Find the LCD of the terms in the equation.

Tap for more steps...

Step 3.1

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

$t + 5, 1$

Step 3.2

Remove parentheses.

$t + 5, 1$

Step 3.3

The LCM of one and any expression is the expression.

$t + 5$

Step 4

Multiply each term in $\frac{5}{t + 5} = x$ by $t + 5$ to eliminate the fractions.

Tap for more steps...

Step 4.1

Multiply each term in $\frac{5}{t + 5} = x$ by $t + 5$ .

$\frac{5}{t + 5} (t + 5) = x (t + 5)$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $t + 5$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{5}{t + 5} (t + 5) = x (t + 5)$

Step 4.2.1.2

Rewrite the expression.

$5 = x (t + 5)$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Apply the distributive property.

$5 = x t + x \cdot 5$

Step 4.3.2

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

$5 = x t + 5 x$

Step 5

Solve the equation.

Tap for more steps...

Step 5.1

Rewrite the equation as $x t + 5 x = 5$ .

$x t + 5 x = 5$

Step 5.2

Subtract $5 x$ from both sides of the equation.

$x t = 5 - 5 x$

Step 5.3

Divide each term in $x t = 5 - 5 x$ by $x$ and simplify.

Tap for more steps...

Step 5.3.1

Divide each term in $x t = 5 - 5 x$ by $x$ .

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

Step 5.3.2

Simplify the left side.

Tap for more steps...

Step 5.3.2.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 5.3.2.1.1

Cancel the common factor.

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

Step 5.3.2.1.2

Divide $t$ by $1$ .

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

Step 5.3.3

Simplify the right side.

Tap for more steps...

Step 5.3.3.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 5.3.3.1.1

Cancel the common factor.

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

Step 5.3.3.1.2

Divide $- 5$ by $1$ .

$t = \frac{5}{x} - 5$

Step 6

Replace $t$ in the equation for $y$ to get the equation in terms of $x$ .

$y = (\frac{5}{x} - 5) + 5$

Step 7

Remove parentheses.

$y = \frac{5}{x} - 5 + 5$

Step 8

Remove parentheses.

$y = (\frac{5}{x} - 5) + 5$

Step 9

Combine the opposite terms in $(\frac{5}{x} - 5) + 5$ .

Tap for more steps...

Step 9.1

Add $- 5$ and $5$ .

$y = \frac{5}{x} + 0$

Step 9.2

Add $\frac{5}{x}$ and $0$ .

$y = \frac{5}{x}$