Simplify (6x+21)/(x^2+5x+4)-5/(x+1)

$\frac{6 x + 21}{x^{2} + 5 x + 4} - \frac{5}{x + 1}$

Simplify each term.

Factor $3$ out of $6 x + 21$ .

Factor $3$ out of $6 x$ .

$\frac{3 (2 x) + 21}{x^{2} + 5 x + 4} - \frac{5}{x + 1}$

Factor $3$ out of $21$ .

$\frac{3 (2 x) + 3 (7)}{x^{2} + 5 x + 4} - \frac{5}{x + 1}$

Factor $3$ out of $3 (2 x) + 3 (7)$ .

$\frac{3 (2 x + 7)}{x^{2} + 5 x + 4} - \frac{5}{x + 1}$

Factor $x^{2} + 5 x + 4$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $4$ and whose sum is $5$ .

$1, 4$

Write the factored form using these integers.

$\frac{3 (2 x + 7)}{(x + 1) (x + 4)} - \frac{5}{x + 1}$

To write $- \frac{5}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x + 4}{x + 4}$ .

$\frac{3 (2 x + 7)}{(x + 1) (x + 4)} - \frac{5}{x + 1} \cdot \frac{x + 4}{x + 4}$

Simplify terms.

Multiply $\frac{5}{x + 1}$ by $\frac{x + 4}{x + 4}$ .

$\frac{3 (2 x + 7)}{(x + 1) (x + 4)} - \frac{5 (x + 4)}{(x + 1) (x + 4)}$

Combine the numerators over the common denominator.

$\frac{3 (2 x + 7) - 5 (x + 4)}{(x + 1) (x + 4)}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 (2 x) + 3 \cdot 7 - 5 (x + 4)}{(x + 1) (x + 4)}$

Multiply $2$ by $3$ .

$\frac{6 x + 3 \cdot 7 - 5 (x + 4)}{(x + 1) (x + 4)}$

Multiply $3$ by $7$ .

$\frac{6 x + 21 - 5 (x + 4)}{(x + 1) (x + 4)}$

Apply the distributive property.

$\frac{6 x + 21 - 5 x - 5 \cdot 4}{(x + 1) (x + 4)}$

Multiply $- 5$ by $4$ .

$\frac{6 x + 21 - 5 x - 20}{(x + 1) (x + 4)}$

Subtract $5 x$ from $6 x$ .

$\frac{x + 21 - 20}{(x + 1) (x + 4)}$

Subtract $20$ from $21$ .

$\frac{x + 1}{(x + 1) (x + 4)}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{x + 1}{(x + 1) (x + 4)}$

Rewrite the expression.

$\frac{1}{x + 4}$

Simplify (6x+21)/(x^2+5x+4)-5/(x+1)

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