Finite Math Examples

$x^{2} y - y = 6$

Step 1

Factor $y$ out of $x^{2} y - y$ .

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Step 1.1

Factor $y$ out of $x^{2} y$ .

$y x^{2} - y = 6$

Step 1.2

Factor $y$ out of $- y$ .

$y x^{2} + y \cdot - 1 = 6$

Step 1.3

Factor $y$ out of $y x^{2} + y \cdot - 1$ .

$y (x^{2} - 1) = 6$

Step 2

Rewrite $1$ as $1^{2}$ .

$y (x^{2} - 1^{2}) = 6$

Step 3

Factor.

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Step 3.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$y ((x + 1) (x - 1)) = 6$

Step 3.2

Remove unnecessary parentheses.

$y (x + 1) (x - 1) = 6$

Step 4

Divide each term in $y (x + 1) (x - 1) = 6$ by $(x + 1) (x - 1)$ and simplify.

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Step 4.1

Divide each term in $y (x + 1) (x - 1) = 6$ by $(x + 1) (x - 1)$ .

$\frac{y (x + 1) (x - 1)}{(x + 1) (x - 1)} = \frac{6}{(x + 1) (x - 1)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x + 1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{y (x + 1) (x - 1)}{(x + 1) (x - 1)} = \frac{6}{(x + 1) (x - 1)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{y (x - 1)}{x - 1} = \frac{6}{(x + 1) (x - 1)}$

Step 4.2.2

Cancel the common factor of $x - 1$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{y (x - 1)}{x - 1} = \frac{6}{(x + 1) (x - 1)}$

Step 4.2.2.2

Divide $y$ by $1$ .

$y = \frac{6}{(x + 1) (x - 1)}$