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PART 2!!

Topic: Addition and Subtraction of polynomials

Directions: Simplify each rational expressions​

PART 2!! Topic: Addition and Subtraction of polynomials Directions: Simplify each-example-1
User Agim
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2 Answers

22 votes
22 votes

Explanation:

4.


= \frac{5ab}{ {a}^(2) - {b}^(2) } - (a - b)/(a + b)


= \frac{5ab}{ {a}^(2) - {b}^(2) } - \frac{(a - b)(a - b)}{ {a}^(2) - {b}^(2) }


= \frac{5ab}{ {a}^(2) - {b}^(2) } - \frac{ {a}^(2) - 2ab + {b}^(2) }{ {a}^(2) - {b}^(2) }


= \frac{5ab - ( {a}^(2) - 2ab + {b}^(2) ) }{ {a}^(2) - {b}^(2) }


= \frac{5ab - {a}^(2) + 2ab - {b}^(2) }{ {a}^(2) - {b}^(2) }


= \frac{7ab - {a}^(2) - {b}^(2) }{ {a}^(2) - {b}^(2) }


\:

5.


= (5)/(n + 5) + (4n)/(2n + 6)


= (5)/(n + 5) + (4n)/(2(n + 3))


= (5)/(n + 5) + (2n)/(n + 3)


= \frac{5(n + 3) + 2(n + 5)}{ {n}^(2) + 8n + 15 }


= \frac{5n + 15 + 2n + 10}{ {n}^(2) + 8n + 15}


= \frac{7n + 25}{ {n}^(2) + 8n + 15}

User Skylar Brown
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10 votes
10 votes


{ \qquad\qquad\huge\underline{{\sf Answer}}}

Let's solve these problems ~

Problem 1 ~


\qquad \sf  \dashrightarrow \: \frac{5ab}{ {a}^(2) - {b}^(2) } - (a - b)/(a + b)


\qquad \sf  \dashrightarrow \: (5ab)/( (a + b)(a - b) ) - (a - b)/(a + b)


\qquad \sf  \dashrightarrow \: (5ab - (a - b)(a - b))/( (a + b)(a - b) )


\qquad \sf  \dashrightarrow \: \frac{5ab - (a - b) {}^(2) }{ {a}^(2) - b {}^(2) }


\qquad \sf  \dashrightarrow \: \frac{5ab - (a {}^(2) - 2ab + {b}^(2) ) {}^{} }{ {a}^(2) - b {}^(2) }


\qquad \sf  \dashrightarrow \: \frac{5ab - a {}^(2) + 2ab - {b}^(2) {}^{} }{ {a}^(2) - b {}^(2) }


\qquad \sf  \dashrightarrow \: \frac{7ab - a {}^(2) - {b}^(2) {}^{} }{ {a}^(2) - b {}^(2) }

Problem 2 ~


\qquad \sf  \dashrightarrow \: (5)/(n + 5) + (4n)/(2n + 6)


\qquad \sf  \dashrightarrow \: (5(2n + 6) + 4n(n + 5))/((2n + 6)(n + 5))


\qquad \sf  \dashrightarrow \: \frac{10n +30 + 4n {}^(2) + 20n}{2n {}^(2) + 10n + 6n +30}


\qquad \sf  \dashrightarrow \: \frac{4n {}^(2) + 30n + 30}{2n {}^(2) + 16n + 30}

[ taking 2 common out ]


{ \qquad \sf  \dashrightarrow \: \frac{2n {}^(2) + 15n + 15}{n {}^(2) + 8n + 15}}

User Ismar Slomic
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2.4k points