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3 years ago

Add or subtract as indicated

Mathematics

1 answer:

Aliun [14]3 years ago

5 0

Option B: $\frac{11x-9}{x^2-1}$ is the correct answer

Step-by-step explanation:

Given

$\frac{5}{x+1} + \frac{6}{x-1} -\frac{10}{x^2-1}$

Simplifying x^2-1

$x^2-1 = (x+1)(x-1)$

So,

$\frac{5}{x+1} + \frac{6}{x-1} -\frac{10}{(x+1)(x-1)}\\=\frac{5(x-1)+6(x+1)-10}{(x+1)(x-1)}\\=\frac{5x-5+6x+6-10}{(x+1)(x-1)}\\=\frac{5x+6x-5+6-10}{(x+1)(x-1)}\\=\frac{11x-9}{(x+1)(x-1)}\\=\frac{11x-9}{x^2-1}$

Hence,

Option B: $\frac{11x-9}{x^2-1}$ is the correct answer

Keywords: Fractions, polynomials

Learn more about polynomials at:

#LearnwithBrainly

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3 years ago

Which function represents a vertical stretch of an exponential function?

nika2105 [10]

Answer:

A. $f(x)=3(\frac{1}{2})^x$

Step-by-step explanation:

The options are:

$A. f(x)=3(\frac{1}{2})^x\\\\B. f(x)=\frac{1}{2}(3)^x\\\\C. f(x)=(3)^{2x}\\\\ D. f(x)=3^{(\frac{1}{2}x)}$

For this exercise it is important to remember that, by definition, the Exponential parent functions have the form shown below:

$f(x) = a^x$

Where "a" is the base.

There are several transformations for a function f(x), some of those transformations are shown below:

1. If $bf(x)$ and $b>1$ , then the function is stretched vertically by a factor of "b".

2. If $bf(x)$ and $0$ , then the function is compressed vertically by a factor of "b"

Therefore, based on the information given above, you can identify that the function that represents a vertical stretch of an Exponential function, is the one given in the Option A. This is:

$f(x)=3(\frac{1}{2})^x$

Where the factor is:

$b=3$