Simplify (2x+3)/(x-8)+(3x+7)/(x-1)

$\frac{2 x + 3}{x - 8} + \frac{3 x + 7}{x - 1}$

To write $\frac{2 x + 3}{x - 8}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{2 x + 3}{x - 8} \cdot \frac{x - 1}{x - 1} + \frac{3 x + 7}{x - 1}$

To write $\frac{3 x + 7}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

$\frac{2 x + 3}{x - 8} \cdot \frac{x - 1}{x - 1} + \frac{3 x + 7}{x - 1} \cdot \frac{x - 8}{x - 8}$

Write each expression with a common denominator of $(x - 8) (x - 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x + 3}{x - 8}$ by $\frac{x - 1}{x - 1}$ .

$\frac{(2 x + 3) (x - 1)}{(x - 8) (x - 1)} + \frac{3 x + 7}{x - 1} \cdot \frac{x - 8}{x - 8}$

Multiply $\frac{3 x + 7}{x - 1}$ by $\frac{x - 8}{x - 8}$ .

$\frac{(2 x + 3) (x - 1)}{(x - 8) (x - 1)} + \frac{(3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Reorder the factors of $(x - 8) (x - 1)$ .

$\frac{(2 x + 3) (x - 1)}{(x - 1) (x - 8)} + \frac{(3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Combine the numerators over the common denominator.

$\frac{(2 x + 3) (x - 1) + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Simplify the numerator.

Expand $(2 x + 3) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$\frac{2 x (x - 1) + 3 (x - 1) + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Apply the distributive property.

$\frac{2 x \cdot x + 2 x \cdot - 1 + 3 (x - 1) + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Apply the distributive property.

$\frac{2 x \cdot x + 2 x \cdot - 1 + 3 x + 3 \cdot - 1 + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$\frac{2 (x \cdot x) + 2 x \cdot - 1 + 3 x + 3 \cdot - 1 + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Multiply $x$ by $x$ .

$\frac{2 x^{2} + 2 x \cdot - 1 + 3 x + 3 \cdot - 1 + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Multiply $- 1$ by $2$ .

$\frac{2 x^{2} - 2 x + 3 x + 3 \cdot - 1 + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Multiply $3$ by $- 1$ .

$\frac{2 x^{2} - 2 x + 3 x - 3 + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Add $- 2 x$ and $3 x$ .

$\frac{2 x^{2} + x - 3 + (3 x + 7) (x - 8)}{(x - 1) (x - 8)}$

Expand $(3 x + 7) (x - 8)$ using the FOIL Method.

Apply the distributive property.

$\frac{2 x^{2} + x - 3 + 3 x (x - 8) + 7 (x - 8)}{(x - 1) (x - 8)}$

Apply the distributive property.

$\frac{2 x^{2} + x - 3 + 3 x \cdot x + 3 x \cdot - 8 + 7 (x - 8)}{(x - 1) (x - 8)}$

Apply the distributive property.

$\frac{2 x^{2} + x - 3 + 3 x \cdot x + 3 x \cdot - 8 + 7 x + 7 \cdot - 8}{(x - 1) (x - 8)}$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$\frac{2 x^{2} + x - 3 + 3 (x \cdot x) + 3 x \cdot - 8 + 7 x + 7 \cdot - 8}{(x - 1) (x - 8)}$

Multiply $x$ by $x$ .

$\frac{2 x^{2} + x - 3 + 3 x^{2} + 3 x \cdot - 8 + 7 x + 7 \cdot - 8}{(x - 1) (x - 8)}$

Multiply $- 8$ by $3$ .

$\frac{2 x^{2} + x - 3 + 3 x^{2} - 24 x + 7 x + 7 \cdot - 8}{(x - 1) (x - 8)}$

Multiply $7$ by $- 8$ .

$\frac{2 x^{2} + x - 3 + 3 x^{2} - 24 x + 7 x - 56}{(x - 1) (x - 8)}$

Add $- 24 x$ and $7 x$ .

$\frac{2 x^{2} + x - 3 + 3 x^{2} - 17 x - 56}{(x - 1) (x - 8)}$

Add $2 x^{2}$ and $3 x^{2}$ .

$\frac{5 x^{2} + x - 3 - 17 x - 56}{(x - 1) (x - 8)}$

Subtract $17 x$ from $x$ .

$\frac{5 x^{2} - 16 x - 3 - 56}{(x - 1) (x - 8)}$

Subtract $56$ from $- 3$ .

$\frac{5 x^{2} - 16 x - 59}{(x - 1) (x - 8)}$

Simplify (2x+3)/(x-8)+(3x+7)/(x-1)

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