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zhenek [66]
2 years ago
9

What is the difference?

Mathematics
1 answer:
AfilCa [17]2 years ago
3 0

Answer:

Option b) is correct.

The difference of given expression is

\left(\frac{2x+5}{x^2-3x}\right)-\left(\frac{3x+5}{x^3-9x}\right)-\left(\frac{1x+1}{x^2-9}\right)=\frac{(x+2)(x+5)}{(x^3-9x)}

Step-by-step explanation:

Given expression is

\left(\frac{2x+5}{x^2-3x}\right)-\left(\frac{3x+5}{x^3-9x}\right)-\left(\frac{1x+1}{x^2-9}\right)

To find their difference

\left(\frac{2x+5}{x^2-3x}\right)-\left(\frac{3x+5}{x^3-9x}\right)-\left(\frac{x+1}{x^2-9}\right)

The expression can be written as below

\left(\frac{2x+5}{x^2-3x}\right)-\left(\frac{3x+5}{x^3-9x}\right)-\left(\frac{x+1}{x^2-9}\right)=\left(\frac{2x+5}{x (x-3)}\right)-\left(\frac{3x+5}{x(x^2-9)}\right)-\left(\frac{x+1}{x^2-9}\right)

=\left(\frac{2x+5}{x(x-3)}\right)-\left(\frac{3x+5}{x(x^2-3^2)}\right)-\left(\frac{x+1}{x^2-3^2}\right)

=\left(\frac{2x+5}{x(x-3)}\right)-\left(\frac{3x+5}{x(x+3)(x-3)}\right)-\left(\frac{x+1}{(x+3)(x-3)}\right) (using a^2-b^2=(a+b)(a-b))

=\frac{(2x+5)(x+3)-(3x+5)-(x+1)x}{x(x+3)(x-3)}

=\frac{2x^2+6x+5x+15-3x-5-x^2-x}{x(x+3)(x-3)}

=\frac{x^2+7x+10}{x(x+3)(x-3)}

=\frac{(x+2)(x+5)}{x(x+3)(x-3)}

=\frac{(x+2)(x+5)}{x(x^2-3^2)}   (using a^2-b^2=(a+b)(a-b))

=\frac{(x+2)(x+5)}{x(x^2-9)}

=\frac{(x+2)(x+5)}{(x^3-9x)}

Therefore \left(\frac{2x+5}{x^2-3x}\right)-\left(\frac{3x+5}{x^3-9x}\right)-\left(\frac{1x+1}{x^2-9}\right)=\frac{(x+2)(x+5)}{(x^3-9x)}

Option b) is correct.

The difference of given expression is

\left(\frac{2x+5}{x^2-3x}\right)-\left(\frac{3x+5}{x^3-9x}\right)-\left(\frac{1x+1}{x^2-9}\right)=\frac{(x+2)(x+5)}{(x^3-9x)}

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y=3/5*x+17

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2 years ago
A 3-meter roll of red ribbon costs $1.89. What is the unit price?
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Step-by-step explanation:

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Compute the lower Riemann sum for the given function f(x)=x2 over the interval x∈[−1,1] with respect to the partition P=[−1,− 1
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21/64

Step-by-step explanation:

First, we need to note that the function f(x) = x² is increasing on (0, +∞), and it is decreasing on (-∞,0)

The first interval generated by the partition is [-1, -1/2], since f is decreasing for negative values, we have that f takes its minimum values at the right extreme of the interval, hence -1/2.

The second interval is [-1/2, 1/2]. Here f takes its minimum value at 0, because f(0) = 0, and f is positive otherwise.

Since f is increasing for positive values of x, then, on the remaining 2 intervals, f takes its minimum value at their respective left extremes, in other words, 1/2 and 3/4 respectively.

We obtain the lower Riemman sum by multiplying this values evaluated in f by the lenght of their respective intervals and summing the results, thus

LP(f) = f(-1/2) * ((-1/2) - (-1)) + f(0) * (1/2 - (-1/2)) + f(1/2)* (3/4 - 1/2) + f(3/4) * (1- 3/4)

= 1/4 * 1/2 + 0 * 1 + 1/4 * 1/4 + 9/16 * 1/4 = 1/8 + 0 + 1/16 + 9/64 = 21/64

As a result, the lower Riemann sum on the partition P is 21/64

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3 years ago
Simplify -8 + 17n + 10 + 8n
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3 years ago
What is the sum? StartFraction 3 Over x squared minus 9 EndFraction StartFraction 5 Over x 3 EndFraction.
V125BC [204]

The sum of the two fractional number, which consist in the variable <em>x</em> is in the polynomial function,

f(x)=\dfrac{5x-12}{(x+3)(x-3)}

<h3>What is the sum of fraction number?</h3>

Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator.

Fraction number are written as,

\dfrac{a}{b}

Here (a) is the numerator and (b) is the denominator.

To find the sum of two fraction numbers, cross multiply both the numbers or find the least common factor as denominator.

The first fraction number given in the problem is,

\dfrac{3}{x^2+9}

The second fraction number given in the problem is,

\dfrac{5}{x+3}

Let the sum of these number is f(x). Thus,

f(x)=\dfrac{3}{x^2-9}+\dfrac{5}{x+3}\\f(x)=\dfrac{3}{(x+3)(x-3)}+\dfrac{5}{x+3}\\

Solve it further as,

f(x)=\dfrac{3+5(x-3)}{(x+3)(x-3)}\\f(x)=\dfrac{3+5x-15}{(x+3)(x-3)}\\f(x)=\dfrac{5x-12}{(x+3)(x-3)}

Thus, the sum of the two fractional number is,

f(x)=\dfrac{5x-12}{(x+3)(x-3)}

Learn more about the fraction number here:

brainly.com/question/78672

6 0
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