$$ \frac{w+3}{w+1}-1=\frac{w-5}{w-7} $$ If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

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Solve the equation $$ \frac{w+3}{w+1}-1=\frac{w-5}{w-7} $$.
Solve the equation by following steps:
- step0: Solve for $$w$$:
  $$\frac{w+3}{w+1}-1=\frac{w-5}{w-7}$$
- step1: Find the domain:
  $$\frac{w+3}{w+1}-1=\frac{w-5}{w-7},w \in \left(-\infty,-1ight)\cup \left(-1,7ight)\cup \left(7,+\inftyight)$$
- step2: Multiply both sides of the equation by LCD:
  $$\left(\frac{w+3}{w+1}-1ight)\left(w+1ight)\left(w-7ight)=\frac{w-5}{w-7}	imes \left(w+1ight)\left(w-7ight)$$
- step3: Simplify the equation:
  $$2w-14=w\left(w+1ight)-5\left(w+1ight)$$
- step4: Calculate:
  $$2w-14=w^{2}+w-5w-5$$
- step5: Simplify:
  $$2w-14=w^{2}-4w-5$$
- step6: Move the expression to the left side:
  $$2w-14-\left(w^{2}-4w-5ight)=0$$
- step7: Subtract the terms:
  $$6w-9-w^{2}=0$$
- step8: Factor the expression:
  $$-\left(3-wight)^{2}=0$$
- step9: Divide the terms:
  $$\left(3-wight)^{2}=0$$
- step10: Simplify the expression:
  $$3-w=0$$
- step11: Move the constant to the right side:
  $$-w=0-3$$
- step12: Remove 0:
  $$-w=-3$$
- step13: Change the signs:
  $$w=3$$
- step14: Check if the solution is in the defined range:
  $$w=3,w \in \left(-\infty,-1ight)\cup \left(-1,7ight)\cup \left(7,+\inftyight)$$
- step15: Find the intersection:
  $$w=3$$
The solution to the equation $$ \frac{w+3}{w+1}-1=\frac{w-5}{w-7} $$ is $$ w=3 $$.
$$ w=3 $$

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

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