Simplify (x^2+6x)/(5x+2)+2/(5x+2)-(x^2+x)/(5x+2)

$\frac{x^{2} + 6 x}{5 x + 2} + \frac{2}{5 x + 2} - \frac{x^{2} + x}{5 x + 2}$

Step 1

Combine the numerators over the common denominator.

$\frac{x^{2} + 6 x + 2 - (x^{2} + x)}{5 x + 2}$

Step 2

Apply the distributive property.

$\frac{x^{2} + 6 x + 2 - x^{2} - x}{5 x + 2}$

Step 3

Combine the opposite terms in $x^{2} + 6 x + 2 - x^{2} - x$ .

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

$\frac{6 x + 2 + 0 - x}{5 x + 2}$

Add $6 x + 2$ and $0$ .

$\frac{6 x + 2 - x}{5 x + 2}$

Step 4

Subtract $x$ from $6 x$ .

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

Step 5

Cancel the common factor of $5 x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$1$