Simplify 4/3xy+4y-2(5/6xy+y-1)-(-1)

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

Step 1

Simplify each term.

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

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

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

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

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

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

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

Simplify each term.

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

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

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

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

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

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

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

Apply the distributive property.

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

Simplify.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 2$ by $- 1$ .

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

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

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

Multiply $- 1$ by $- 1$ .

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

Step 2

Simplify terms.

Combine the numerators over the common denominator.

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

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

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

Move the negative in front of the fraction.

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

Subtract $2 y$ from $4 y$ .

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

Simplify the expression.

Add $2$ and $1$ .

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

Move $3$ .

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

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

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

Simplify 4/3xy+4y-2(5/6xy+y-1)-(-1)

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