Simplify (2/(5t)-3/(3t))/(1/(2t)+1/(2t))

$\frac{\frac{2}{5 t} - \frac{3}{3 t}}{\frac{1}{2 t} + \frac{1}{2 t}}$

Step 1

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\frac{2}{5 t} - \frac{3}{3 t}}{\frac{1}{2 t} + \frac{1}{2 t}}$

Rewrite the expression.

$\frac{\frac{2}{5 t} - \frac{1}{t}}{\frac{1}{2 t} + \frac{1}{2 t}}$

Step 2

Multiply the numerator and denominator of the complex fraction by $10 t$ .

Multiply $\frac{\frac{2}{5 t} - \frac{1}{t}}{\frac{1}{2 t} + \frac{1}{2 t}}$ by $\frac{10 t}{10 t}$ .

$\frac{10 t}{10 t} \cdot \frac{\frac{2}{5 t} - \frac{1}{t}}{\frac{1}{2 t} + \frac{1}{2 t}}$

Combine.

$\frac{10 t (\frac{2}{5 t} - \frac{1}{t})}{10 t (\frac{1}{2 t} + \frac{1}{2 t})}$

Step 3

Apply the distributive property.

$\frac{10 t \frac{2}{5 t} + 10 t (- \frac{1}{t})}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Step 4

Simplify by cancelling.

Cancel the common factor of $5 t$ .

Factor $5 t$ out of $10 t$ .

$\frac{5 t (2) \frac{2}{5 t} + 10 t (- \frac{1}{t})}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Cancel the common factor.

$\frac{5 t \cdot 2 \frac{2}{5 t} + 10 t (- \frac{1}{t})}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Rewrite the expression.

$\frac{2 \cdot 2 + 10 t (- \frac{1}{t})}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Multiply $2$ by $2$ .

$\frac{4 + 10 t (- \frac{1}{t})}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Cancel the common factor of $t$ .

Move the leading negative in $- \frac{1}{t}$ into the numerator.

$\frac{4 + 10 t \frac{- 1}{t}}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Factor $t$ out of $10 t$ .

$\frac{4 + t \cdot 10 \frac{- 1}{t}}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Cancel the common factor.

$\frac{4 + t \cdot 10 \frac{- 1}{t}}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Rewrite the expression.

$\frac{4 + 10 \cdot - 1}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Multiply $10$ by $- 1$ .

$\frac{4 - 10}{10 t \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Cancel the common factor of $2 t$ .

Factor $2 t$ out of $10 t$ .

$\frac{4 - 10}{2 t (5) \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Cancel the common factor.

$\frac{4 - 10}{2 t \cdot 5 \frac{1}{2 t} + 10 t \frac{1}{2 t}}$

Rewrite the expression.

$\frac{4 - 10}{5 + 10 t \frac{1}{2 t}}$

Cancel the common factor of $2 t$ .

Factor $2 t$ out of $10 t$ .

$\frac{4 - 10}{5 + 2 t (5) \frac{1}{2 t}}$

Cancel the common factor.

$\frac{4 - 10}{5 + 2 t \cdot 5 \frac{1}{2 t}}$

Rewrite the expression.

$\frac{4 - 10}{5 + 5}$

Step 5

Reduce the expression by cancelling the common factors.

Subtract $10$ from $4$ .

$\frac{- 6}{5 + 5}$

Add $5$ and $5$ .

$\frac{- 6}{10}$

Cancel the common factor of $- 6$ and $10$ .

Factor $2$ out of $- 6$ .

$\frac{2 (- 3)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 \cdot - 3}{2 \cdot 5}$

Cancel the common factor.

$\frac{2 \cdot - 3}{2 \cdot 5}$

Rewrite the expression.

$\frac{- 3}{5}$

Move the negative in front of the fraction.

$- \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{5}$

Decimal Form:

$- 0.6$

Simplify (2/(5t)-3/(3t))/(1/(2t)+1/(2t))

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