Alright students, let's simplify the expression step-by-step:
[tex]\[
-15 x^2 - 8 y^2 + \frac{22 x y}{2 y} - 3 x
\][/tex]
1. Identify and simplify the division:
- We need to simplify [tex]\(\frac{22 x y}{2 y}\)[/tex].
Notice that [tex]\( y \)[/tex] in the numerator and the denominator can cancel each other out:
[tex]\[
\frac{22 x y}{2 y} = \frac{22 x}{2}
\][/tex]
2. Simplify the resulting fraction:
- Simplify [tex]\(\frac{22 x}{2}\)[/tex]:
[tex]\[
\frac{22 x}{2} = 11 x
\][/tex]
3. Substitute back into the original expression:
- Now we replace [tex]\(\frac{22 x y}{2 y}\)[/tex] with [tex]\(11 x\)[/tex]:
[tex]\[
-15 x^2 - 8 y^2 + 11 x - 3 x
\][/tex]
4. Combine like terms:
- Notice that the [tex]\( x \)[/tex]-terms can be combined:
[tex]\[
11 x - 3 x = 8 x
\][/tex]
5. Rewrite the expression:
- The expression now simplifies to:
[tex]\[
-15 x^2 - 8 y^2 + 8 x
\][/tex]
The simplified form of the original expression is thus:
[tex]\[
-15 x^2 + 11 x y^2 - 3 x - 8 y^2
\][/tex]
