simplify
make into one fraction:
-2+(11/(x-2))+(-7/(x-2)^2)

To simplify the expression:

\[
-2 + \frac{11}{x - 2} + \frac{-7}{(x - 2)^2}
\]

we need to find a common denominator for all terms. The common denominator will be \((x - 2)^2\), since it is the highest power of the denominator in the expression.

### Steps:
1. Rewrite \(-2\) and \(\frac{11}{x - 2}\) to have the common denominator \((x - 2)^2\).

\[
-2 = \frac{-2(x - 2)^2}{(x - 2)^2}
\]
\[
\frac{11}{x - 2} = \frac{11(x - 2)}{(x - 2)^2}
\]

2. Now, substitute everything into one fraction:

\[
\frac{-2(x - 2)^2 + 11(x - 2) - 7}{(x - 2)^2}
\]

3. Expand the numerator:

\[
-2(x - 2)^2 = -2(x^2 - 4x + 4) = -2x^2 + 8x - 8
\]
\[
11(x - 2) = 11x - 22
\]

Now substitute them into the numerator:

\[
\frac{(-2x^2 + 8x - 8) + (11x - 22) - 7}{(x - 2)^2}
\]

4. Combine like terms:

\[
\frac{-2x^2 + (8x + 11x) - (8 + 22 + 7)}{(x - 2)^2}
\]
\[
\frac{-2x^2 + 19x - 37}{(x - 2)^2}
\]

### Final Answer:
\[
\frac{-2x^2 + 19x - 37}{(x - 2)^2}
\]

Would you like a detailed breakdown of any step, or have any other questions?

Here are 5 related questions:
1. How do you find the least common denominator between rational expressions?
2. How do you expand a binomial like \((x - 2)^2\)?
3. How would the simplification change if the exponents were higher, like \((x - 2)^3\)?
4. How can factoring help in simplifying rational expressions?
5. How do you simplify expressions with three or more fractions?

**Tip:** Always check if you can factor the numerator or denominator further to simplify expressions!

simplify make into one fraction: -2+(11/(x-2))+(-7/(x-2)^2)

Learn how to simplify the expression -2 + 11/(x-2) + (-7/(x-2)^2) into a single fraction. This solution involves finding a common denominator, expanding binomials, and simplifying rational expressions. Suitable for students in Grades 9-12.

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