Calculus Examples

$x = t - 2$ , $y = \frac{t}{t - 2}$

Step 1

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

$x = t - 2$

Step 2

Rewrite the equation as $t - 2 = x$ .

$t - 2 = x$

Step 3

Add $2$ to both sides of the equation.

$t = x + 2$

Step 4

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

$y = \frac{x + 2}{(x + 2) - 2}$

Step 5

Remove parentheses.

$y = \frac{x + 2}{x + 2 - 2}$

Step 6

Remove parentheses.

$y = \frac{x + 2}{(x + 2) - 2}$

Step 7

Simplify the denominator.

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Step 7.1

Subtract $2$ from $2$ .

$y = \frac{x + 2}{x + 0}$

Step 7.2

Add $x$ and $0$ .

$y = \frac{x + 2}{x}$