Evaluate (3/5x+3/4)-(1/3x-1/8)

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

Step 1

Simplify each term.

Combine $\frac{3}{5}$ and $x$ .

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

Combine $\frac{1}{3}$ and $x$ .

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

Apply the distributive property.

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

Multiply $- - \frac{1}{8}$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{1}{8}$ by $1$ .

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

Step 2

To write $\frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

To write $- \frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $3$ .

$\frac{3 x \cdot 3}{15} - \frac{x}{3} \cdot \frac{5}{5} + \frac{3}{4} + \frac{1}{8}$

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

$\frac{3 x \cdot 3}{15} - \frac{x \cdot 5}{3 \cdot 5} + \frac{3}{4} + \frac{1}{8}$

Multiply $3$ by $5$ .

$\frac{3 x \cdot 3}{15} - \frac{x \cdot 5}{15} + \frac{3}{4} + \frac{1}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - x \cdot 5}{15} + \frac{3}{4} + \frac{1}{8}$

Step 6

Find the common denominator.

Multiply $\frac{3 x \cdot 3 - x \cdot 5}{15}$ by $\frac{8}{8}$ .

$\frac{3 x \cdot 3 - x \cdot 5}{15} \cdot \frac{8}{8} + \frac{3}{4} + \frac{1}{8}$

Multiply $\frac{3 x \cdot 3 - x \cdot 5}{15}$ by $\frac{8}{8}$ .

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

Multiply $\frac{3}{4}$ by $\frac{30}{30}$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{15 \cdot 8} + \frac{3}{4} \cdot \frac{30}{30} + \frac{1}{8}$

Multiply $\frac{3}{4}$ by $\frac{30}{30}$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{15 \cdot 8} + \frac{3 \cdot 30}{4 \cdot 30} + \frac{1}{8}$

Multiply $\frac{1}{8}$ by $\frac{15}{15}$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{15 \cdot 8} + \frac{3 \cdot 30}{4 \cdot 30} + \frac{1}{8} \cdot \frac{15}{15}$

Multiply $\frac{1}{8}$ by $\frac{15}{15}$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{15 \cdot 8} + \frac{3 \cdot 30}{4 \cdot 30} + \frac{15}{8 \cdot 15}$

Reorder the factors of $15 \cdot 8$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{8 \cdot 15} + \frac{3 \cdot 30}{4 \cdot 30} + \frac{15}{8 \cdot 15}$

Multiply $8$ by $15$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{120} + \frac{3 \cdot 30}{4 \cdot 30} + \frac{15}{8 \cdot 15}$

Multiply $4$ by $30$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{120} + \frac{3 \cdot 30}{120} + \frac{15}{8 \cdot 15}$

Multiply $8$ by $15$ .

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8}{120} + \frac{3 \cdot 30}{120} + \frac{15}{120}$

Step 7

Combine the numerators over the common denominator.

$\frac{(3 x \cdot 3 - x \cdot 5) \cdot 8 + 3 \cdot 30 + 15}{120}$

Step 8

Simplify each term.

Multiply $3$ by $3$ .

$\frac{(9 x - x \cdot 5) \cdot 8 + 3 \cdot 30 + 15}{120}$

Multiply $5$ by $- 1$ .

$\frac{(9 x - 5 x) \cdot 8 + 3 \cdot 30 + 15}{120}$

Subtract $5 x$ from $9 x$ .

$\frac{4 x \cdot 8 + 3 \cdot 30 + 15}{120}$

Multiply $8$ by $4$ .

$\frac{32 x + 3 \cdot 30 + 15}{120}$

Multiply $3$ by $30$ .

$\frac{32 x + 90 + 15}{120}$

Step 9

Add $90$ and $15$ .

$\frac{32 x + 105}{120}$

Evaluate (3/5x+3/4)-(1/3x-1/8)

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