Algebra Examples

$y > x y < - x$

Step 1

Solve $y > x y$ for $y$ .

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Step 1.1

Subtract $x y$ from both sides of the inequality.

$y - x y > 0$

Step 1.2

Factor $y$ out of $y - x y$ .

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Step 1.2.1

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

$y \cdot 1 - x y > 0$

Step 1.2.2

Factor $y$ out of $- x y$ .

$y \cdot 1 + y (- x) > 0$

Step 1.2.3

Factor $y$ out of $y \cdot 1 + y (- x)$ .

$y (1 - x) > 0$

$y (1 - x) > 0$

Step 1.3

Divide each term in $y (1 - x) > 0$ by $1 - x$ and simplify.

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Step 1.3.1

Divide each term in $y (1 - x) > 0$ by $1 - x$ .

$\frac{y (1 - x)}{1 - x} > \frac{0}{1 - x}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $1 - x$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{y (1 - x)}{1 - x} > \frac{0}{1 - x}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y > \frac{0}{1 - x}$

$y > \frac{0}{1 - x}$

$y > \frac{0}{1 - x}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $0$ by $1 - x$ .

$y > 0$

$y > 0$

$y > 0$

$y > 0$

Step 2

Divide each term in $x y < - x$ by $x$ and simplify.

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Step 2.1

Divide each term in $x y < - x$ by $x$ .

$\frac{x y}{x} < \frac{- x}{x}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x y}{x} < \frac{- x}{x}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y < \frac{- x}{x}$

$y < \frac{- x}{x}$

$y < \frac{- x}{x}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $x$ .

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Step 2.3.1.1

Cancel the common factor.

$y < \frac{- x}{x}$

Step 2.3.1.2

Divide $- 1$ by $1$ .

$y < - 1$

$y < - 1$

$y < - 1$

$y < - 1$

Step 3

Find the intersection of $y > 0$ and $y < - 1$ .

No solution

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$