Question

Simplify
please solve this...​

Answer 1

y-1/y^2 +4y

Explanation:

2y - 1/y x (y + 4) - y-2/y^2 +4y - 2y -8

2y-1/y x (y+4 - y-2/y x (y +4 ) - 2(y + 4)

2y -1 / y x (y+4) - y-2/(y+4) x (y-2)

2y-1/y x (y+4) - 1/y +4

2y -1 -y/y x (y + 4)

y-1/y^2 +4y

Answer 2

`(y-1)/(y(y+4))`

Explanation:

Given expression:

`\implies (2y-1)/(y^2+4y)-(y-2)/(y^2+2y-8)`

Factor the denominators of both fractions:

`\implies (2y-1)/(y(y+4))-(y-2)/(y^2+4y-2y-8)`

`\implies (2y-1)/(y(y+4))-(y-2)/(y(y+4)-2(y+4))`

`\implies (2y-1)/(y(y+4))-(y-2)/((y-2)(y+4))`

Cancel the common factor (y - 2) of the right fraction:

`\implies (2y-1)/(y(y+4))-(1)/((y+4))`

Adjust the fractions based on the LCM of y(y + 4):

`\implies (2y-1)/(y(y+4))-(y)/(y(y+4))`

`\textsf{Apply the fraction rule} \quad (a)/(c)-(b)/(c)=(a-b)/(c):`

`\implies (2y-1-y)/(y(y+4))`

Simplify:

`\implies (y-1)/(y(y+4))`