divide and simplify
(y^3-3y)/(y^2-9)divided by
(y^2-7y-30)/(y^2+6y+9)
Please help!
(y^3-3y)/(y^2-9)*(y^2+6y+9)/(y^2-7y-30)=
(y(y^2-3)/(y+3)(y-3))*(y+3)(y+3)/(y+3)(y-10)=((y^2-3)/(y-3)*1/(y-10)=
(y^2-3)/(y-3)(y-10)
NOTE: All "(y+3)s" cancelled.
To divide and simplify the given expression, we need to follow these steps:
Step 1: Factor both the numerators and the denominators.
For the first expression, (y^3-3y)/(y^2-9), factor the numerator and denominator as follows:
Numerator: y^3 - 3y = y(y^2 - 3)
Denominator: y^2 - 9 = (y - 3)(y + 3)
For the second expression, (y^2-7y-30)/(y^2+6y+9), factor the numerator and denominator as follows:
Numerator: y^2 - 7y - 30 = (y - 10)(y + 3)
Denominator: y^2 + 6y + 9 = (y + 3)(y + 3)
Step 2: Rewrite the division as multiplication by the reciprocal.
Now, we can rewrite the expression as multiplication by the reciprocal:
[(y^3-3y)/(y^2-9)] * [(y^2+6y+9)/(y^2-7y-30)]
Step 3: Cancel out common factors.
Next, we cancel out common factors between the numerator and denominator:
(y^3 - 3y) / (y^2 - 9) * (y^2 + 6y + 9) / (y^2 - 7y - 30)
Since (y^2 - 9) and (y^2 + 6y + 9) both have the factor (y + 3), we can cancel it out:
(y^3 - 3y) / 1 * 1 / (y^2 - 7y - 30)
Simplifying further, we have:
(y^3 - 3y) / (y^2 - 7y - 30)
And that is the simplified expression.