Resolver 2-5a+6/2+7a+6:(2a+10/a+1-a-1)+1/a+3]*2a^2+5a-3/2a^2

$$\frac { 2 - 5 a + 6 } { 2 + 7 a + 6 } : ( \frac { 2 a + 10 } { a + 1 } - a - 1 ) + \frac { 1 } { a + 3 } ] \cdot \frac { 2 a ^ { 2 } + 5 a - 3 } { 2 a ^ { 2 } }$$

Calcular

$$\frac{4\left(3a^{2}-4a-8\right)}{\left(7a+8\right)\left(a^{2}-9\right)}$$

Pasos de solución curta

Suma 2 e 6 para obter 8.

$$\frac{\frac{8-5a}{2+7a+6}}{\frac{2a+10}{a+1}-a-1}+\frac{1}{a+3}$$

Suma 2 e 6 para obter 8.

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10}{a+1}-a-1}+\frac{1}{a+3}$$

Para sumar ou restar expresións, expándeas para facer que os seus denominadores sexan iguais. Multiplica -a-1 por \frac{a+1}{a+1}.

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10}{a+1}+\frac{\left(-a-1\right)\left(a+1\right)}{a+1}}+\frac{1}{a+3}$$

Dado que \frac{2a+10}{a+1} e \frac{\left(-a-1\right)\left(a+1\right)}{a+1} teñen o mesmo denominador, súmaos mediante a suma dos seus numeradores.

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10+\left(-a-1\right)\left(a+1\right)}{a+1}}+\frac{1}{a+3}$$

Fai as multiplicacións en 2a+10+\left(-a-1\right)\left(a+1\right).

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10-a^{2}-a-a-1}{a+1}}+\frac{1}{a+3}$$

Combina como termos en 2a+10-a^{2}-a-a-1.

$$\frac{\frac{8-5a}{8+7a}}{\frac{9-a^{2}}{a+1}}+\frac{1}{a+3}$$

Divide \frac{8-5a}{8+7a} entre \frac{9-a^{2}}{a+1} mediante a multiplicación de \frac{8-5a}{8+7a} polo recíproco de \frac{9-a^{2}}{a+1}.

$$\frac{\left(8-5a\right)\left(a+1\right)}{\left(8+7a\right)\left(9-a^{2}\right)}+\frac{1}{a+3}$$

Factoriza \left(8+7a\right)\left(9-a^{2}\right).

$$\frac{\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(-a-3\right)\left(7a+8\right)}+\frac{1}{a+3}$$

Para sumar ou restar expresións, expándeas para facer que os seus denominadores sexan iguais. O mínimo común múltiplo de \left(a-3\right)\left(-a-3\right)\left(7a+8\right) e a+3 é \left(a-3\right)\left(a+3\right)\left(7a+8\right). Multiplica \frac{\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(-a-3\right)\left(7a+8\right)} por \frac{-1}{-1}. Multiplica \frac{1}{a+3} por \frac{\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(7a+8\right)}.

$$\frac{-\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}+\frac{\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Dado que \frac{-\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)} e \frac{\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)} teñen o mesmo denominador, súmaos mediante a suma dos seus numeradores.

$$\frac{-\left(8-5a\right)\left(a+1\right)+\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Fai as multiplicacións en -\left(8-5a\right)\left(a+1\right)+\left(a-3\right)\left(7a+8\right).

$$\frac{-8a-8+5a^{2}+5a+7a^{2}+8a-21a-24}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Combina como termos en -8a-8+5a^{2}+5a+7a^{2}+8a-21a-24.

$$\frac{-16a-32+12a^{2}}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Expande \left(a-3\right)\left(a+3\right)\left(7a+8\right).

$$\frac{-16a-32+12a^{2}}{7a^{3}+8a^{2}-63a-72}$$

Expandir

$$-\frac{4\left(3a^{2}-4a-8\right)}{\left(7a+8\right)\left(9-a^{2}\right)}$$

Pasos de solución curta

Suma 2 e 6 para obter 8.

$$\frac{\frac{8-5a}{2+7a+6}}{\frac{2a+10}{a+1}-a-1}+\frac{1}{a+3}$$

Suma 2 e 6 para obter 8.

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10}{a+1}-a-1}+\frac{1}{a+3}$$

Para sumar ou restar expresións, expándeas para facer que os seus denominadores sexan iguais. Multiplica -a-1 por \frac{a+1}{a+1}.

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10}{a+1}+\frac{\left(-a-1\right)\left(a+1\right)}{a+1}}+\frac{1}{a+3}$$

Dado que \frac{2a+10}{a+1} e \frac{\left(-a-1\right)\left(a+1\right)}{a+1} teñen o mesmo denominador, súmaos mediante a suma dos seus numeradores.

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10+\left(-a-1\right)\left(a+1\right)}{a+1}}+\frac{1}{a+3}$$

Fai as multiplicacións en 2a+10+\left(-a-1\right)\left(a+1\right).

$$\frac{\frac{8-5a}{8+7a}}{\frac{2a+10-a^{2}-a-a-1}{a+1}}+\frac{1}{a+3}$$

Combina como termos en 2a+10-a^{2}-a-a-1.

$$\frac{\frac{8-5a}{8+7a}}{\frac{9-a^{2}}{a+1}}+\frac{1}{a+3}$$

Divide \frac{8-5a}{8+7a} entre \frac{9-a^{2}}{a+1} mediante a multiplicación de \frac{8-5a}{8+7a} polo recíproco de \frac{9-a^{2}}{a+1}.

$$\frac{\left(8-5a\right)\left(a+1\right)}{\left(8+7a\right)\left(9-a^{2}\right)}+\frac{1}{a+3}$$

Factoriza \left(8+7a\right)\left(9-a^{2}\right).

$$\frac{\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(-a-3\right)\left(7a+8\right)}+\frac{1}{a+3}$$

Para sumar ou restar expresións, expándeas para facer que os seus denominadores sexan iguais. O mínimo común múltiplo de \left(a-3\right)\left(-a-3\right)\left(7a+8\right) e a+3 é \left(a-3\right)\left(a+3\right)\left(7a+8\right). Multiplica \frac{\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(-a-3\right)\left(7a+8\right)} por \frac{-1}{-1}. Multiplica \frac{1}{a+3} por \frac{\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(7a+8\right)}.

$$\frac{-\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}+\frac{\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Dado que \frac{-\left(8-5a\right)\left(a+1\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)} e \frac{\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)} teñen o mesmo denominador, súmaos mediante a suma dos seus numeradores.

$$\frac{-\left(8-5a\right)\left(a+1\right)+\left(a-3\right)\left(7a+8\right)}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Fai as multiplicacións en -\left(8-5a\right)\left(a+1\right)+\left(a-3\right)\left(7a+8\right).

$$\frac{-8a-8+5a^{2}+5a+7a^{2}+8a-21a-24}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Combina como termos en -8a-8+5a^{2}+5a+7a^{2}+8a-21a-24.

$$\frac{-16a-32+12a^{2}}{\left(a-3\right)\left(a+3\right)\left(7a+8\right)}$$

Expande \left(a-3\right)\left(a+3\right)\left(7a+8\right).

$$\frac{-16a-32+12a^{2}}{7a^{3}+8a^{2}-63a-72}$$