Solve for $$ y $$ $$ \frac{4}{y+4}=\frac{8}{2 y+8}-3 $$

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UpStudy AI · Accepted Answer

Solve the equation $$ \frac{4}{y+4}=\frac{8}{2y+8}-3 $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$\frac{4}{y+4}=\frac{8}{2y+8}-3$$
- step1: Find the domain:
  $$\frac{4}{y+4}=\frac{8}{2y+8}-3,y
eq -4$$
- step2: Divide the terms:
  $$\frac{4}{y+4}=\frac{4}{y+4}-3$$
- step3: Multiply both sides of the equation by LCD:
  $$\frac{4}{y+4}	imes \left(y+4ight)=\left(\frac{4}{y+4}-3ight)\left(y+4ight)$$
- step4: Simplify the equation:
  $$4=-8-3y$$
- step5: Swap the sides:
  $$-8-3y=4$$
- step6: Move the constant to the right side:
  $$-3y=4+8$$
- step7: Add the numbers:
  $$-3y=12$$
- step8: Change the signs:
  $$3y=-12$$
- step9: Divide both sides:
  $$\frac{3y}{3}=\frac{-12}{3}$$
- step10: Divide the numbers:
  $$y=-4$$
- step11: Check if the solution is in the defined range:
  $$y=-4,y
eq -4$$
- step12: Find the intersection:
  $$y \in \varnothing $$
The solution to the equation $$ \frac{4}{y+4}=\frac{8}{2y+8}-3 $$ is that there are no real solutions for $$ y $$.
There are no real solutions for $$ y $$.

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