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Yuri [45]
3 years ago
14

Simplyfy (x - 5 / x^3 + 27) + (2 / x^2 - 9)

Mathematics
2 answers:
BARSIC [14]3 years ago
5 0
\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\ \quad \\
\textit{difference of cubes}
\\ \quad \\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
(a+b)(a^2-ab+b^2)= a^3+b^3 \\\\
-------------------------------\\\\

\bf \cfrac{x-5}{x^3+27}+\cfrac{2}{x^2-9}\implies \cfrac{x-5}{x^3+3^3}+\cfrac{2}{x^2-3^2}
\\\\\\
\cfrac{x-5}{(x+3)(x^2-3x+3^2)}+\cfrac{2}{(x-3)(x+3)}\\\\\\
\cfrac{x-5}{(x+3)(x^2-3x+9)}+\cfrac{2}{(x-3)(x+3)}
\\\\\\
\textit{so, we'll use the LCD of }(x-3)(x+3)(x^2-3x+9)
\\\\\\
\cfrac{(x-3)(x-5)~~+~~(x^2-3x+9)2}{(x-3)(x+3)(x^2-3x+9)}
\\\\\\
\cfrac{x^2-8x+15~~+~~2x^2-6x+18}{(x-3)(x+3)(x^2-3x+9)}\implies \cfrac{3x^2-14x+33}{(x-3)(x+3)(x^2-3x+9)}
Maksim231197 [3]3 years ago
3 0
The answer simplified should be x-5/x^3+18+2/x^2. Hope that is helpful.
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3 0
3 years ago
Margo brought 7 pens from a book store some pens cost $3.00 EACH and the rest cost $4.00 . If she paid a total of 23.00 for the
Montano1993 [528]

Answer:

5

Step-by-step explanation:

Margo bought 7 pens for $23.

Some pens are $3 and some $4.

We need to find how many $3 pens she bought.

Let the number of $3 pens be represented by p and let the number of $3 pens be represented by r. So:

p = $3  and r = $4

Now we know 7 pens were purchased so is we add the number of $3 pens purchased to the number of $4 pens purchased, we will get 7.

p + r = 7

We know that the total cost of the pens is $23 so that equation would be found by takign the $3 pen multiplied by the number of $3 pens purchsed added to the $4 pen multiplied by the number of $4 pens purchsed, which equals $23.

$3p + $4r = $23

Now we have 2 equations and 2 unknowns.

p + r = 7

$3p + $4r = $23

Let's solve for r in the first equation.

p + r = 7     Subtract p from both sides.

p - p + r = 7 - p   The p on the left cancels.

r = 7 - p

Now that we know r, we can substitute it into the second equation and solve for p.

$3p + $4r = $23

3p + 4( 7 - p) = 23       Multiply it out.

3p + 4*7 - 4*p = $23

3p + 28 - 4p = 23      Combine like terms.

3p  - 4p + 28 = 23

- 1p + 28 = 23       Subtract 28 from both sides.

- p + 28 - 28 = 23 - 28  

- p = - 5   Divide each side by -1

- p/- 1 = - 5/ - 1       The negative cancels on each side.

p = 5

We can see Margo bought 5 $3 pens.

For fun, let's solve for how many $4 pens she bought. We know p, so we plug it in the first equation and solve for r.

p + r = 7

5 + r = 7  Subtract 5 from each side

5 - 5 + r = 7 - 5

r = 7 - 5

r = 2

So Margo bought 5 $3 pens and 2 $4 pens!

8 0
2 years ago
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