Algebra Examples

$\frac{4}{3} x y + 4 y - 2 (\frac{5}{6} x y + y - 1) - (- 1)$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{4}{3} (x y)$ .

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Step 1.1.1

Combine $x$ and $\frac{4}{3}$ .

$\frac{x \cdot 4}{3} y + 4 y - 2 (\frac{5}{6} \cdot (x y) + y - 1) - (- 1)$

Step 1.1.2

Combine $\frac{x \cdot 4}{3}$ and $y$ .

$\frac{x \cdot 4 y}{3} + 4 y - 2 (\frac{5}{6} \cdot (x y) + y - 1) - (- 1)$

Step 1.2

Move $4$ to the left of $x$ .

$\frac{4 \cdot x y}{3} + 4 y - 2 (\frac{5}{6} \cdot (x y) + y - 1) - (- 1)$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $\frac{5}{6} (x y)$ .

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Step 1.3.1.1

Combine $x$ and $\frac{5}{6}$ .

$\frac{4 x y}{3} + 4 y - 2 (\frac{x \cdot 5}{6} y + y - 1) - (- 1)$

Step 1.3.1.2

Combine $\frac{x \cdot 5}{6}$ and $y$ .

$\frac{4 x y}{3} + 4 y - 2 (\frac{x \cdot 5 y}{6} + y - 1) - (- 1)$

Step 1.3.2

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

$\frac{4 x y}{3} + 4 y - 2 (\frac{5 x y}{6} + y - 1) - (- 1)$

Step 1.4

Apply the distributive property.

$\frac{4 x y}{3} + 4 y - 2 \frac{5 x y}{6} - 2 y - 2 \cdot - 1 - (- 1)$

Step 1.5

Simplify.

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Step 1.5.1

Cancel the common factor of $2$ .

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Step 1.5.1.1

Factor $2$ out of $- 2$ .

$\frac{4 x y}{3} + 4 y + 2 (- 1) \frac{5 x y}{6} - 2 y - 2 \cdot - 1 - (- 1)$

Step 1.5.1.2

Factor $2$ out of $6$ .

$\frac{4 x y}{3} + 4 y + 2 \cdot - 1 \frac{5 x y}{2 \cdot 3} - 2 y - 2 \cdot - 1 - (- 1)$

Step 1.5.1.3

Cancel the common factor.

$\frac{4 x y}{3} + 4 y + 2 \cdot - 1 \frac{5 x y}{2 \cdot 3} - 2 y - 2 \cdot - 1 - (- 1)$

Step 1.5.1.4

Rewrite the expression.

$\frac{4 x y}{3} + 4 y - 1 \frac{5 x y}{3} - 2 y - 2 \cdot - 1 - (- 1)$

Step 1.5.2

Multiply $- 2$ by $- 1$ .

$\frac{4 x y}{3} + 4 y - 1 \frac{5 x y}{3} - 2 y + 2 - (- 1)$

Step 1.6

Rewrite $- 1 \frac{5 x y}{3}$ as $- \frac{5 x y}{3}$ .

$\frac{4 x y}{3} + 4 y - \frac{5 x y}{3} - 2 y + 2 - (- 1)$

Step 1.7

Multiply $- 1$ by $- 1$ .

$\frac{4 x y}{3} + 4 y - \frac{5 x y}{3} - 2 y + 2 + 1$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$4 y - 2 y + 2 + 1 + \frac{4 x y - 5 x y}{3}$

Step 2.2

Subtract $5 x y$ from $4 x y$ .

$4 y - 2 y + 2 + 1 + \frac{- x y}{3}$

Step 2.3

Move the negative in front of the fraction.

$4 y - 2 y + 2 + 1 - \frac{x y}{3}$

Step 2.4

Subtract $2 y$ from $4 y$ .

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

Step 2.5

Simplify the expression.

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Step 2.5.1

Add $2$ and $1$ .

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

Step 2.5.2

Move $3$ .

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

Step 2.5.3

Reorder $2 y$ and $- \frac{x y}{3}$ .

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