Verified Answer :

Louli

Answer:
\(\frac{y(y+2)}{(y+1)}\)

Explanation:
When multiplying fractions, we multiply the numerators together and the denominator together and then we simplify.

The given expression is:
\(\frac{y^2}{y-3} * \frac{y^2-y-6}{y^2+y}\)

Let's consider the second fraction given:
\(\frac{y^2-y-6}{y^2+y}\)
We can do the following:
1- factor the numerator
2- take y as a common factor from the denominator
Doing this, we will end up with the following fraction:
\(\frac{(y-3)(y+2)}{y(y+1)}\)

The expression now became:
\(\frac{y^2}{y-3} * \frac{(y-3)(y+2)}{y(y+1)}\)

We can now multiply the numerators together and the denominator together as follows:
\(\frac{y^2}{y-3} * \frac{(y-3)(y+2)}{y(y+1)}\) = \(\frac{y^2(y-3)(y+2)}{y(y+1)(y-3)}\)

Finally, we can note that we can perform the following on the resultant expression:
1- divide both the numerator and denominator by (y-3)
2- divide both the numerator and denominator by (y)
Doing this, we will end up with:
\(\frac{y(y+2)}{(y+1)}\)

Since no further simplification can be done, therefore, our final expression is:
\(\frac{y(y+2)}{(y+1)}\)

Hope this helps :)

Answer:

the product of given expression \(\frac{y^2}{y-3}\) and  \(\frac{y^2-y-6}{y^2+y}\) is \(\frac{y(y+2)}{(y+1)},y eq -1\)

Step-by-step explanation:

 Consider the given expression \(\frac{y^2}{y-3}\) and  \(\frac{y^2-y-6}{y^2+y}\)

We have to write the product of given expressions  in simplest form,

We solve the two terms separately,

Consider the second expression

\(\frac{y^2-y-6}{y^2+y}\)

Taking y common from denominator we have  \(\frac{y^2-y-6}{y(y+1)}\)

Numerator consist of a quadratic equation,  \({y^2-y-6}\)

We can solve it using middle term splitting method,

-y can be written as 2y -3y

Thus, it becomes,

\({y^2-y-6}=y^2+2y-3y-6\)

Taking y common from first two terms and -3 common from last two terms we have,

\(y^2+2y-3y-6=y(y+2)-3(y+2)=(y-3)(y+2)\)

thus, the second expression becomes ,

\(\frac{y^2-y-6}{y(y+1)}=\frac{(y-3)(y+2)}{y(y+1)}\)

Now , we multiply the two expression ,we get,

\(\Rightarrow \frac{y^2}{y-3}\times \frac{y^2-y-6}{y^2+y}\)

\(\Rightarrow \frac{y^2}{y-3}\times \frac{(y-3)(y+2)}{y(y+1)}\)

Simplifying , we get,

\(\Rightarrow y \times \frac{(y+2)}{(y+1)}\\\\\\ \Rightarrow\frac{y(y+2)}{(y+1)},y eq -1\)

Thus, the product of given expression \(\frac{y^2}{y-3}\) and  \(\frac{y^2-y-6}{y^2+y}\) is \(\frac{y(y+2)}{(y+1)},y eq -1\)

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