Question

Consider the difference below.
x-3/x^2-x-5 - 5/8x
Place the steps require to simplify the given difference of two expressions into one, simplified rational expression in the correct order.

Answer 1

Answer:

(-(5 x^3 + 40 x^2 + 24))/(8 x^2) - I can't read the picture yousend it's way to small.

Step-by-step explanation:

Simplify the following:

x - (5 x)/8 - x - 5 - 3/x^2

Put each term in x - (5 x)/8 - x - 5 - 3/x^2 over the common denominator 8 x^2: x - (5 x)/8 - x - 5 - 3/x^2 = (8 x^3)/(8 x^2) - (5 x^3)/(8 x^2) - (8 x^3)/(8 x^2) - (40 x^2)/(8 x^2) - 24/(8 x^2):

(8 x^3)/(8 x^2) - (5 x^3)/(8 x^2) - (8 x^3)/(8 x^2) - (40 x^2)/(8 x^2) - 24/(8 x^2)

(8 x^3)/(8 x^2) - (5 x^3)/(8 x^2) - (8 x^3)/(8 x^2) - (40 x^2)/(8 x^2) - 24/(8 x^2) = (8 x^3 - 5 x^3 - 8 x^3 - 40 x^2 - 24)/(8 x^2):

(8 x^3 - 5 x^3 - 8 x^3 - 40 x^2 - 24)/(8 x^2)

Grouping like terms, 8 x^3 - 5 x^3 - 8 x^3 - 40 x^2 - 24 = (8 x^3 - 8 x^3 - 5 x^3) - 40 x^2 - 24:

((8 x^3 - 8 x^3 - 5 x^3) - 40 x^2 - 24)/(8 x^2)

8 x^3 - 8 x^3 - 5 x^3 = -5 x^3:

(-5 x^3 - 40 x^2 - 24)/(8 x^2)

Factor -1 out of -5 x^3 - 40 x^2 - 24:

Answer: (-(5 x^3 + 40 x^2 + 24))/(8 x^2)