Algebra Examples

$\frac{- 7 x y}{3 x} + \frac{4 y^{2}}{2 y}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $x$ .

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Step 1.1.1

Cancel the common factor.

$\frac{- 7 x y}{3 x} + \frac{4 y^{2}}{2 y}$

Step 1.1.2

Rewrite the expression.

$\frac{- 7 y}{3} + \frac{4 y^{2}}{2 y}$

$\frac{- 7 y}{3} + \frac{4 y^{2}}{2 y}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{7 y}{3} + \frac{4 y^{2}}{2 y}$

Step 1.3

Cancel the common factor of $4$ and $2$ .

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Step 1.3.1

Factor $2$ out of $4 y^{2}$ .

$- \frac{7 y}{3} + \frac{2 (2 y^{2})}{2 y}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $2 y$ .

$- \frac{7 y}{3} + \frac{2 (2 y^{2})}{2 (y)}$

Step 1.3.2.2

Cancel the common factor.

$- \frac{7 y}{3} + \frac{2 (2 y^{2})}{2 y}$

Step 1.3.2.3

Rewrite the expression.

$- \frac{7 y}{3} + \frac{2 y^{2}}{y}$

$- \frac{7 y}{3} + \frac{2 y^{2}}{y}$

$- \frac{7 y}{3} + \frac{2 y^{2}}{y}$

Step 1.4

Cancel the common factor of $y^{2}$ and $y$ .

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Step 1.4.1

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

$- \frac{7 y}{3} + \frac{y (2 y)}{y}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Raise $y$ to the power of $1$ .

$- \frac{7 y}{3} + \frac{y (2 y)}{y^{1}}$

Step 1.4.2.2

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

$- \frac{7 y}{3} + \frac{y (2 y)}{y \cdot 1}$

Step 1.4.2.3

Cancel the common factor.

$- \frac{7 y}{3} + \frac{y (2 y)}{y \cdot 1}$

Step 1.4.2.4

Rewrite the expression.

$- \frac{7 y}{3} + \frac{2 y}{1}$

Step 1.4.2.5

Divide $2 y$ by $1$ .

$- \frac{7 y}{3} + 2 y$

$- \frac{7 y}{3} + 2 y$

$- \frac{7 y}{3} + 2 y$

$- \frac{7 y}{3} + 2 y$

Step 2

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7 y}{3} + 2 y \cdot \frac{3}{3}$

Step 3

Simplify terms.

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Step 3.1

Combine $2 y$ and $\frac{3}{3}$ .

$- \frac{7 y}{3} + \frac{2 y \cdot 3}{3}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 7 y + 2 y \cdot 3}{3}$

$\frac{- 7 y + 2 y \cdot 3}{3}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $y$ out of $- 7 y + 2 y \cdot 3$ .

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Step 4.1.1

Factor $y$ out of $- 7 y$ .

$\frac{y \cdot - 7 + 2 y \cdot 3}{3}$

Step 4.1.2

Factor $y$ out of $2 y \cdot 3$ .

$\frac{y \cdot - 7 + y (2 \cdot 3)}{3}$

Step 4.1.3

Factor $y$ out of $y \cdot - 7 + y (2 \cdot 3)$ .

$\frac{y (- 7 + 2 \cdot 3)}{3}$

$\frac{y (- 7 + 2 \cdot 3)}{3}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{y (- 7 + 6)}{3}$

Step 4.3

Add $- 7$ and $6$ .

$\frac{y \cdot - 1}{3}$

$\frac{y \cdot - 1}{3}$

Step 5

Simplify the expression.

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Step 5.1

Move $- 1$ to the left of $y$ .

$\frac{- 1 \cdot y}{3}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{y}{3}$

$- \frac{y}{3}$

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