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