Solve for $$ y $$. $$ \frac{7}{y^{2}+7 y+12}=\frac{1}{y+4}-\frac{5}{y+3} $$ If there is more than one solution, separate them with If there is no solution, click on "No solution".

Question

UpStudy AI · Accepted Answer

Solve the equation $$ \frac{7}{y^{2}+7y+12}=\frac{1}{y+4}-\frac{5}{y+3} $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$\frac{7}{y^{2}+7y+12}=\frac{1}{y+4}-\frac{5}{y+3}$$
- step1: Find the domain:
  $$\frac{7}{y^{2}+7y+12}=\frac{1}{y+4}-\frac{5}{y+3},y \in \left(-\infty,-4ight)\cup \left(-4,-3ight)\cup \left(-3,+\inftyight)$$
- step2: Multiply both sides of the equation by LCD:
  $$\frac{7}{y^{2}+7y+12}	imes \left(y^{2}+7y+12ight)=\left(\frac{1}{y+4}-\frac{5}{y+3}ight)\left(y^{2}+7y+12ight)$$
- step3: Simplify the equation:
  $$7=-4y-17$$
- step4: Swap the sides:
  $$-4y-17=7$$
- step5: Move the constant to the right side:
  $$-4y=7+17$$
- step6: Add the numbers:
  $$-4y=24$$
- step7: Change the signs:
  $$4y=-24$$
- step8: Divide both sides:
  $$\frac{4y}{4}=\frac{-24}{4}$$
- step9: Divide the numbers:
  $$y=-6$$
- step10: Check if the solution is in the defined range:
  $$y=-6,y \in \left(-\infty,-4ight)\cup \left(-4,-3ight)\cup \left(-3,+\inftyight)$$
- step11: Find the intersection:
  $$y=-6$$
The solution to the equation is $$ y = -6 $$.
$$ y = -6 $$

Solve for .

If there is more than one solution, separate them with
If there is no solution, click on “No solution”.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions

Solve for . If there is more than one solution, separate them with If there is no solution, click on “No solution”.