Simplify (3/5x^2-4/5x+2/5)+(x-2/5x^2+7/5)

$(\frac{3}{5} x^{2} - \frac{4}{5} x + \frac{2}{5}) + (x - \frac{2}{5} x^{2} + \frac{7}{5})$

Step 1

Combine fractions.

Remove parentheses.

$\frac{3}{5} x^{2} - \frac{4}{5} x + \frac{2}{5} + x - \frac{2}{5} x^{2} + \frac{7}{5}$

Combine the numerators over the common denominator.

$\frac{3}{5} x^{2} - \frac{4}{5} x + x - \frac{2}{5} x^{2} + \frac{2 + 7}{5}$

Add $2$ and $7$ .

$\frac{3}{5} x^{2} - \frac{4}{5} x + x - \frac{2}{5} x^{2} + \frac{9}{5}$

Step 2

Simplify each term.

Combine $\frac{3}{5}$ and $x^{2}$ .

$\frac{3 x^{2}}{5} - \frac{4}{5} x + x - \frac{2}{5} x^{2} + \frac{9}{5}$

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

$\frac{3 x^{2}}{5} - \frac{x \cdot 4}{5} + x - \frac{2}{5} x^{2} + \frac{9}{5}$

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

$\frac{3 x^{2}}{5} - \frac{4 \cdot x}{5} + x - \frac{2}{5} x^{2} + \frac{9}{5}$

Combine $x^{2}$ and $\frac{2}{5}$ .

$\frac{3 x^{2}}{5} - \frac{4 x}{5} + x - \frac{x^{2} \cdot 2}{5} + \frac{9}{5}$

Move $2$ to the left of $x^{2}$ .

$\frac{3 x^{2}}{5} - \frac{4 x}{5} + x - \frac{2 x^{2}}{5} + \frac{9}{5}$

Step 3

Simplify terms.

Combine the numerators over the common denominator.

$x + \frac{3 x^{2} - 4 x - 2 x^{2} + 9}{5}$

Subtract $2 x^{2}$ from $3 x^{2}$ .

$x + \frac{x^{2} - 4 x + 9}{5}$

Step 4

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

$x \cdot \frac{5}{5} + \frac{x^{2} - 4 x + 9}{5}$

Step 5

Simplify terms.

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

$\frac{x \cdot 5}{5} + \frac{x^{2} - 4 x + 9}{5}$

Combine the numerators over the common denominator.

$\frac{x \cdot 5 + x^{2} - 4 x + 9}{5}$

Step 6

Simplify the numerator.

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

$\frac{5 \cdot x + x^{2} - 4 x + 9}{5}$

Subtract $4 x$ from $5 x$ .

$\frac{x^{2} + x + 9}{5}$