Evaluate -3+4/5e=-2+3/2e+1/10e

$- 3 + \frac{4}{5} e = - 2 + \frac{3}{2} e + \frac{1}{10} e$

Combine $\frac{4}{5}$ and $e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3}{2} \cdot e + \frac{1}{10} \cdot e$

Simplify each term.

Combine $\frac{3}{2}$ and $e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e}{2} + \frac{1}{10} \cdot e$

Combine $\frac{1}{10}$ and $e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e}{2} + \frac{e}{10}$

To write $\frac{3 e}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e}{2} \cdot \frac{5}{5} + \frac{e}{10}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 e}{2}$ by $\frac{5}{5}$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e \cdot 5}{2 \cdot 5} + \frac{e}{10}$

Multiply $2$ by $5$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e \cdot 5}{10} + \frac{e}{10}$

Combine the numerators over the common denominator.

$- 3 + \frac{4 e}{5} = - 2 + \frac{3 e \cdot 5 + e}{10}$

Simplify each term.

Simplify the numerator.

Multiply $5$ by $3$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{15 e + e}{10}$

Add $15 e$ and $e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{16 e}{10}$

Cancel the common factor of $16$ and $10$ .

Factor $2$ out of $16 e$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{2 (8 e)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$- 3 + \frac{4 e}{5} = - 2 + \frac{2 (8 e)}{2 (5)}$

Cancel the common factor.

$- 3 + \frac{4 e}{5} = - 2 + \frac{2 (8 e)}{2 \cdot 5}$

Rewrite the expression.

$- 3 + \frac{4 e}{5} = - 2 + \frac{8 e}{5}$