Question

PART 2!!

Topic: Addition and Subtraction of polynomials

Directions: Simplify each rational expressions​

Answer 1

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}`

Answer 2

`{ \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}}`