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S_A_V [24]
3 years ago
6

Subtract rational expression. Show work please.

Mathematics
1 answer:
yan [13]3 years ago
6 0

Given:

$\frac{x+4}{x-1}-\frac{5}{x^{2}-1}

To find:

The simplified rational expression by subtraction.

Solution:

Let us factor x^2-1. It can be written as x^2-1^2.

x^2-1^2=(x-1)(x+1) using algebraic identity.

$\frac{x+4}{x-1}-\frac{5}{x^{2}-1}=\frac{x+4}{x-1}-\frac{5}{(x+1)(x-1)}

LCM of x-1,(x+1)(x-1)=(x+1)(x-1)

Make the denominators same using LCM.

Multiply and divide the first term by (x + 1) to make the denominator same.

                        $=\frac{(x+4)(x+1)}{(x-1)(x+1)}-\frac{5}{(x-1)(x+1)}

Now, denominators are same, you can subtract the fractions.

                        $=\frac{(x+4)(x+1)-5}{(x-1)(x+1)}

Expand (x+4)(x+1)-5.

                        $=\frac{x^2+4x+x+4-5}{(x-1)(x+1)}

                        $=\frac{x^{2}+5 x-1}{(x-1)(x+1)}

$\frac{x+4}{x-1}-\frac{5}{x^{2}-1}=\frac{x^{2}+5 x-1}{(x-1)(x+1)}

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3 years ago
For the function​ below, find a formula for the upper sum obtained by dividing the interval [a comma b ][a,b] into n equal subin
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Answer:

See below

Step-by-step explanation:

We start by dividing the interval [0,4] into n sub-intervals of length 4/n

[0,\displaystyle\frac{4}{n}],[\displaystyle\frac{4}{n},\displaystyle\frac{2*4}{n}],[\displaystyle\frac{2*4}{n},\displaystyle\frac{3*4}{n}],...,[\displaystyle\frac{(n-1)*4}{n},4]

Since f is increasing in the interval [0,4], the upper sum is obtained by evaluating f at the right end of each sub-interval multiplied by 4/n.

Geometrically, these are the areas of the rectangles whose height is f evaluated at the right end of the interval and base 4/n (see picture)

\displaystyle\frac{4}{n}f(\displaystyle\frac{1*4}{n})+\displaystyle\frac{4}{n}f(\displaystyle\frac{2*4}{n})+...+\displaystyle\frac{4}{n}f(\displaystyle\frac{n*4}{n})=\\\\=\displaystyle\frac{4}{n}((\displaystyle\frac{1*4}{n})^2+3+(\displaystyle\frac{2*4}{n})^2+3+...+(\displaystyle\frac{n*4}{n})^2+3)=\\\\\displaystyle\frac{4}{n}((1^2+2^2+...+n^2)\displaystyle\frac{4^2}{n^2}+3n)=\\\\\displaystyle\frac{4^3}{n^3}(1^2+2^2+...+n^2)+12

but  

1^2+2^2+...+n^2=\displaystyle\frac{n(n+1)(2n+1)}{6}

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\displaystyle\frac{4^3}{n^3}(1^2+2^2+...+n^2)+12=\displaystyle\frac{4^3}{n^3}\displaystyle\frac{n(n+1)(2n+1)}{6}+12=\\\\\displaystyle\frac{4^3}{6}(2+\displaystyle\frac{3}{n}+\displaystyle\frac{1}{n^2})+12

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\displaystyle\frac{4^3}{3}+12=\displaystyle\frac{100}{3}

8 0
4 years ago
1.what is the volume of the small cone in terms of pi
svp [43]

Step-by-step explanation:

<u>Step 1:  Find the radius of the big cone</u>

\frac{radius_1}{height_1} = \frac{radius_2}{height_2}

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20/ 5=5x / 5

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<u>Step 2:  Find the volume of the small cone</u>

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<u>Step 3:  Find the volume of the large cone</u>

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V=\frac{\pi*4^2*10}{3}

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Vikentia [17]
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x = 180 - 100 - 50
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So x = 30°, and thus option D
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3 years ago
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