Question

Topic: Addition and Subtraction of polynomials

Directions: Simplify each rational expressions

please answer with solution.​

Answer 1

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

Here's your solution :

Problem 1 ~

`\qquad \sf  \dashrightarrow \: \cfrac{r + 6}{3r - 6} + (r + 1)/(3r - 6)`

[ since the denominator is same, we can just add the numerators ]

`\qquad \sf  \dashrightarrow \: \cfrac{r + 6 + r + 1}{3r - 6}`

`\qquad \sf  \dashrightarrow \: \cfrac{2r + 7}{3r - 6}`

Problem 2 ~

`\qquad \sf  \dashrightarrow \: (6)/(x - 1) - (5x)/(4)`

`\qquad \sf  \dashrightarrow \: (6(4) - 5x(x - 1))/(4(x - 1))`

`\qquad \sf  \dashrightarrow \: \frac{24- 5x {}^(2) + 5x}{4x - 4}`

Problem 3 ~

`\qquad \sf  \dashrightarrow \: (2x)/(5x + 4) + (6x)/(2x + 3)`

`\qquad \sf  \dashrightarrow \: (2x(2x + 3) + 6x(5x + 4))/((5x + 4)(2x + 3))`

`\qquad \sf  \dashrightarrow \: \frac{4 {x}^(2) + 6x+ 30 {x}^(2) + 24x}{10 {x}^(2) + 15x + 8x + 12}`

`\qquad \sf  \dashrightarrow \: \frac{34 {x}^(2) + 30x}{10 {x}^(2) + 23 {x}^{} +12 }`