2y 4 +16y 3 2y 3 =start fraction, 2, y, cubed, divided by, 2, y, start superscript, 4, end superscript, plus, 16, y, cubed, end fraction, equals

Step-by-step explanation:

The problem is

To solve this problem let us simplify the denominator by taking the greatest common factor of it

∵ The denominator is

∵ The factors of 2 are 1, 2

∵ The factors of 16 are 1, 2, 4, 8, 16

∴ The common factors of 2 and 16 are 1 and 2

∵ The greatest one is 2

∴ The greatest common factor of 2 and 16 is 2

The greatest common factor of a variable is the variable with the smallest exponent

∵ The smallest exponent of and y³ is 3

∴ The greatest common factor of and y³ is y³

∴ The greatest common factor of and 16y³ is 2y³

Divide each term of the denominator by the greatest common factor

∵ ÷ 2y³ = y

∵ 16y³ ÷ 2y³ = 8

- The factorization of the denominator is 2y³(y + 8)

∴   = 2y³(y + 8)

Substitute it in the fraction

∴  

- Simplify the right hand side by dividing up and down by 2y³

∴  

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: