Simplify (3x+5)/x+7/(x-3)

$\frac{3 x + 5}{x} + \frac{7}{x - 3}$

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

$\frac{3 x + 5}{x} \cdot \frac{x - 3}{x - 3} + \frac{7}{x - 3}$

To write $\frac{7}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3 x + 5}{x} \cdot \frac{x - 3}{x - 3} + \frac{7}{x - 3} \cdot \frac{x}{x}$

Write each expression with a common denominator of $x (x - 3)$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{(3 x + 5) (x - 3)}{x (x - 3)} + \frac{7}{x - 3} \cdot \frac{x}{x}$

Multiply $\frac{7}{x - 3}$ by $\frac{x}{x}$ .

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

Reorder the factors of $(x - 3) x$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Expand $(3 x + 5) (x - 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$\frac{3 x \cdot x + 3 x \cdot - 3 + 5 (x - 3) + 7 x}{x (x - 3)}$

Apply the distributive property.

$\frac{3 x \cdot x + 3 x \cdot - 3 + 5 x + 5 \cdot - 3 + 7 x}{x (x - 3)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{3 (x \cdot x) + 3 x \cdot - 3 + 5 x + 5 \cdot - 3 + 7 x}{x (x - 3)}$

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $3$ .

$\frac{3 x^{2} - 9 x + 5 x + 5 \cdot - 3 + 7 x}{x (x - 3)}$

Multiply $5$ by $- 3$ .

$\frac{3 x^{2} - 9 x + 5 x - 15 + 7 x}{x (x - 3)}$

Add $- 9 x$ and $5 x$ .

$\frac{3 x^{2} - 4 x - 15 + 7 x}{x (x - 3)}$

Add $- 4 x$ and $7 x$ .

$\frac{3 x^{2} + 3 x - 15}{x (x - 3)}$

Factor $3$ out of $3 x^{2} + 3 x - 15$ .

Factor $3$ out of $3 x^{2}$ .

$\frac{3 (x^{2}) + 3 x - 15}{x (x - 3)}$

Factor $3$ out of $3 x$ .

$\frac{3 (x^{2}) + 3 (x) - 15}{x (x - 3)}$

Factor $3$ out of $- 15$ .

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

Factor $3$ out of $3 (x^{2}) + 3 x$ .

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

Factor $3$ out of $3 (x^{2} + x) + 3 \cdot - 5$ .

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

Simplify (3x+5)/x+7/(x-3)

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