What is the quotient of the rational expression below? 3x+1/x+8 : x-7/5x

8x^2 + 45/5x

Step-by-step explanation:

write the division as a fraction

3x + 1/x + 8/x - 7/5x

using a=a/1, convert the expression into a fraction

3x/1 - 7/5x

calculate the product

3x/1 - 7x/5

expand the fraction to get the least common denominator

5 x 3x / 5 x 1 - 7x/5

multiply the numbers

15x/5 - 7x/5

write all numerators above the common denominator

15x - 7x/5

collect like terms

8x/5

write the factor as a product

8/5 x + 1/x + 8/x

calculate the product

8x/5 + 5 x 1/5x + 5 x 8/5x

expand the fraction to get the least common denominator

X x 8x/X x 5 + 5/5x + 5 x 8/5x

multiply the numbers

X x 8x/X x 5 + 5/5x + 40/5x

calculate the product

8x^2/5x + 5/5x + 40/5x

write all numerators above the common denominator

8x^2 + 5 + 40/5x

add the numbers and that's the answer

8x^2 + 45/5x

(that was l o n g)