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QveST [7]
2 years ago
11

What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minu

s 9 x EndFraction minus StartFraction x + 1 Over x squared minus 9 EndFraction StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction StartFraction (x + 5) (x + 4) Over x cubed minus 9 x EndFraction StartFraction negative 2 x + 11 Over x cubed minus 12 x minus 9 EndFraction StartFraction 3 (x + 2) Over x squared minus 3 x EndFraction

Mathematics
2 answers:
Sunny_sXe [5.5K]2 years ago
6 0

Answer:

<h2>\frac{(x + 5)(x + 2)}{ {x}^{3} - 9x }</h2>

First option is the correct option.

Step-by-step explanation:

\frac{2x + 5}{ {x}^{2} - 3x }  -  \frac{3x + 5}{ {x}^{3} - 9x }  -  \frac{x + 1}{ {x}^{2} - 9 }

Factor out X from the expression

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

Using {a}^{2}  -  {b}^{2}  = (a - b)(a + b) , factor the expression

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

Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )

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

Multiply the parentheses

\frac{2 {x}^{2}  + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)}

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

\frac{2 {x}^{2}  + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)}

Distribute -x through the parentheses

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

Using {a}^{2}  -  {b}^{2}  = (a + b)(a - b) , simplify the product

\frac{2 {x}^{2}  + 5x + 6x + 15 - 3x - 5 -  {x}^{2}  - x}{x( {x}^{2}  - 9)}

Collect like terms

\frac{ {x}^{2}  + 7x + 15 - 5}{x( {x}^{2}  - 9)}

Subtract the numbers

\frac{ {x}^{2}  + 7x + 10}{ x({x}^{2}   - 9)}

Distribute x through the parentheses

\frac{ {x}^{2}  + 7x + 10}{ {x}^{3}  - 9x}

Write 7x as a sum

\frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x }

Factor out X from the expression

\frac{x(x + 5) + 2x + 10}{ {x}^{3}  - 9x}

Factor out 2 from the expression

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

Factor out x + 5 from the expression

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

Hope this helps...

Best regards!!

Alex787 [66]2 years ago
3 0

Answer: The Answer is A

Step-by-step explanation: EDGE 2020

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