Simplify (4t-8/5)-(3-4/3t)

$(4 t - \frac{8}{5}) - (3 - \frac{4}{3} t)$

Step 1

Simplify each term.

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

$4 t - \frac{8}{5} - (3 - \frac{t \cdot 4}{3})$

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

$4 t - \frac{8}{5} - (3 - \frac{4 t}{3})$

Apply the distributive property.

$4 t - \frac{8}{5} - 1 \cdot 3 - - \frac{4 t}{3}$

Multiply $- 1$ by $3$ .

$4 t - \frac{8}{5} - 3 - - \frac{4 t}{3}$

Multiply $- - \frac{4 t}{3}$ .

Multiply $- 1$ by $- 1$ .

$4 t - \frac{8}{5} - 3 + 1 \frac{4 t}{3}$

Multiply $\frac{4 t}{3}$ by $1$ .

$4 t - \frac{8}{5} - 3 + \frac{4 t}{3}$

Step 2

To write $4 t$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 t \cdot \frac{3}{3} + \frac{4 t}{3} - \frac{8}{5} - 3$

Step 3

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

$\frac{4 t \cdot 3}{3} + \frac{4 t}{3} - \frac{8}{5} - 3$

Step 4

Combine the numerators over the common denominator.

$\frac{4 t \cdot 3 + 4 t}{3} - \frac{8}{5} - 3$

Step 5

Find the common denominator.

Multiply $\frac{4 t \cdot 3 + 4 t}{3}$ by $\frac{5}{5}$ .

$\frac{4 t \cdot 3 + 4 t}{3} \cdot \frac{5}{5} - \frac{8}{5} - 3$

Multiply $\frac{4 t \cdot 3 + 4 t}{3}$ by $\frac{5}{5}$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{3 \cdot 5} - \frac{8}{5} - 3$

Multiply $\frac{8}{5}$ by $\frac{3}{3}$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{3 \cdot 5} - (\frac{8}{5} \cdot \frac{3}{3}) - 3$

Multiply $\frac{8}{5}$ by $\frac{3}{3}$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{3 \cdot 5} - \frac{8 \cdot 3}{5 \cdot 3} - 3$

Write $- 3$ as a fraction with denominator $1$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{3 \cdot 5} - \frac{8 \cdot 3}{5 \cdot 3} + \frac{- 3}{1}$

Multiply $\frac{- 3}{1}$ by $\frac{15}{15}$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{3 \cdot 5} - \frac{8 \cdot 3}{5 \cdot 3} + \frac{- 3}{1} \cdot \frac{15}{15}$

Multiply $\frac{- 3}{1}$ by $\frac{15}{15}$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{3 \cdot 5} - \frac{8 \cdot 3}{5 \cdot 3} + \frac{- 3 \cdot 15}{15}$

Multiply $3$ by $5$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{15} - \frac{8 \cdot 3}{5 \cdot 3} + \frac{- 3 \cdot 15}{15}$

Reorder the factors of $5 \cdot 3$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{15} - \frac{8 \cdot 3}{3 \cdot 5} + \frac{- 3 \cdot 15}{15}$

Multiply $3$ by $5$ .

$\frac{(4 t \cdot 3 + 4 t) \cdot 5}{15} - \frac{8 \cdot 3}{15} + \frac{- 3 \cdot 15}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{(4 t \cdot 3 + 4 t) \cdot 5 - 8 \cdot 3 - 3 \cdot 15}{15}$

Step 7

Simplify each term.

Multiply $3$ by $4$ .

$\frac{(12 t + 4 t) \cdot 5 - 8 \cdot 3 - 3 \cdot 15}{15}$

Add $12 t$ and $4 t$ .

$\frac{16 t \cdot 5 - 8 \cdot 3 - 3 \cdot 15}{15}$

Multiply $5$ by $16$ .

$\frac{80 t - 8 \cdot 3 - 3 \cdot 15}{15}$

Multiply $- 8$ by $3$ .

$\frac{80 t - 24 - 3 \cdot 15}{15}$

Multiply $- 3$ by $15$ .

$\frac{80 t - 24 - 45}{15}$

Step 8

Subtract $45$ from $- 24$ .

$\frac{80 t - 69}{15}$

Simplify (4t-8/5)-(3-4/3t)

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