Question

Find the sum of the equation

Answer 1

`\frac{{y}^(2)+13y-6}{{(y-1)}^(2)(y+7)}`

Explanation:

1) Rewrite
`{y}^(2)-2y+1y` in the form
`{a}^(2)-2ab+{b}^(2)`, where a = y and b = 1.

`\frac{y}{{y}^(2)-2(y)(1)+{1}^(2)}+\frac{6}{{y}^(2)+6y-7}`

2) Use Square of Difference:
`{(a-b)}^(2)={a}^(2)-2ab+{b}^(2)`.

`\frac{y}{{(y-1)}^(2)}+\frac{6}{{y}^(2)+6y-7}`

3) Factor
`{y}^(2)+6y-7`.

1 - Ask: Which two numbers add up to 6 and multiply to -7?

-1 and 7

2 - Rewrite the expression using the above.

`(y-1)(y-7)`

Outcome/Result:
`(y)/((y-1)^2) +(6)/((y-1)(y+7))`

4) Rewrite the expression with a common denominator.

`\frac{y(y+7)+6(y-1)}{{(y-1)}^(2)(y+7)}`

5) Expand.

`\frac{{y}^(2)+7y+6y-6}{{(y-1)}^(2)(y+7)}`

6) Collect like terms.

`\frac{{y}^(2)+(7y+6y)-6}{{(y-1)}^(2)(y+7)}`

7) Simplify
`{y}^(2)+(7y+6y)-6y` to
`{y}^(2)+13y-6y`

`\frac{{y}^(2)+13y-6}{{(y-1)}^(2)(y+7)}`

Answer 2

`\boldsymbol{(y)/(y^(2)-2y+1 )+(6)/(y^(2)+6y-7 ) \ \ \to \ \ \ Exercise \ to \ solve. }`

Factor y² - 2y + 1. Factor y² + 6y -7.

`\bf{\frac{y}{(y-1){2} }+(6)/((y-1)(y+7)) }`

To add or subtract expressions, expand them so their denominators are the same. The least common multiple of (y - 1)² and (y - 1)(y + 2) it is (x + y)(y - 1)². Multiply
`\bf{(y)/((y-1)^(2) ) }` by
`\bf{(y+7)/(y+7). }` Multiply
`\bf{(6)/((y-1)(y+7)) \ by \ (y-1)/(y-1). }`

`\bf{(y(y+7))/((y+7)(y-1)^(2) )+(6(y-1))/((y+7)(y-1)^(2) ) }`

Since
`\bf{(y(y+7))/((y+7)(y-1)^(2) )\ and \ (6(y-1))/((y+7)(y-1)^(2) ) }` have the same denominator, add their numerators to add them together.

`\bf{(y(y+7)+6(y-1))/((y+7)(y-1)^(2) ) }`

Do the multiplications on y(y + 7) + 6(y - 1).

`\bf{(y^(2) +7+6y-1)/((y+7)(y-1)^(2) ) }`

Combine like terms in y² + 7y + 6y - 6.

`\bf{(13-6y+1)/((y+7)(y-1)^(2) ) }`

xpande (y+7)(y−1)².

`\bf{(13y-6+y^(2) )/(y^(3)+5y^(2)-13y+7 ) \ \ \to \ \ \ Answer }`

`\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}`