Problem

Solve the equation and check your solutions. \[ \frac{y+30}{y+15}-2=\frac{15}{y+15} \] Select the correct choice below and fill in any answer boxes present in your choice A. $y=\square$ (Type an integer or a simplified fraction.) B. There is no solution.

Solution

Step 1 :\[\frac{y+30}{y+15}-2=\frac{15}{y+15}\]

Step 2 :Distribute -2 to the terms in the denominator to simplify the left side of the equation:

Step 3 :\[\frac{y+30-2(y+15)}{y+15}=\frac{15}{y+15}\]

Step 4 :Simplify the numerator on the left side:

Step 5 :\[\frac{-y}{y+15}=\frac{15}{y+15}\]

Step 6 :Since the denominators are the same, set the numerators equal to each other:

Step 7 :\[-y = 15\]

Step 8 :Solving for y gives:

Step 9 :\[y = -15\]

Step 10 :Check this solution in the original equation. If it makes the denominator zero, it is not a valid solution. Substituting y = -15 into the original equation gives:

Step 11 :\[\frac{-15+30}{-15+15}-2=\frac{15}{-15+15}\]

Step 12 :This simplifies to:

Step 13 :\[\frac{15}{0}-2=\frac{15}{0}\]

Step 14 :Since division by zero is undefined, y = -15 is not a valid solution. Therefore, the correct choice is:

Step 15 :\[\boxed{\text{There is no solution}}\]

From Solvely APP
Source: https://solvelyapp.com/problems/FNeqvtJWvR/

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