$f(x)=\dfrac{x-4}{x+9};\ g(x)=\dfrac{x-9}{x+4}\\\\f(x)+g(x)=\dfrac{x-4}{x+9}+\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)+(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2+x^2-9^2}{(x+9)(x+4)}=\dfrac{2x^2-16-81}{(x+9)(x+4)}=\dfrac{2x^2-97}{(x+9)(x+4)}\\\\f(x)-g(x)=\dfrac{x-4}{x+9}-\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)-(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2-(x^2-9^2)}{(x+9)(x+4)}=\dfrac{x^2-16-x^2+81}{(x+9)(x+4)}=\dfrac{65}{(x+9)(x+4)}$

$\dfrac{f+g}{f-g}=(f+g):(f-g)=\dfrac{2x^2-97}{(x+9)(x+4)}:\dfrac{65}{(x+9)(x+4)}\\\\=\dfrac{2x^2-97}{(x+9)(x+4)}\cdot\dfrac{(x+9)(x+4)}{65}\\\\Answer:\ \boxed{\dfrac{f+g}{f-g}=\dfrac{2x^2-97}{65}}$

6 0

3 years ago

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maggie spent 4.50 on cheese and fruit at the farmers market. she bought 1/8 pound of apples, 1/4 pound of pears and 1.25 pounds

serious [3.7K]

The produced answer is 5.5

hope it helps

4 0

3 years ago

Which of the following ratios is equivalent to 49:35?

Arte-miy333 [17]

The best way to find it is to reduce each ratio you work with to its
lowest terms,and see which ones are equal. To reduce a ratio to its
lowest terms, divide each number by their greatest common factor.

First, the one that you're trying to match: 49:35 .
The greatest common factor of 49 and 35 is 7 .
Divide each number by 7 . . . 7:5 . . . that's what you have to match.

7:4
Their greatest common factor is ' 1 '.
No help at all, and this one is not it.

14:25
Again, their greatest common factor is '1 '.
No help at all, and this one is not it.

21:15
Their greatest common factor is ' 3 '.
Divide both numbers by 3 . . . 7:5 .
That's it !

8 0

3 years ago

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