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Question

I need help with multiplying and dividing rational expressions. I need to show work.

1. (4x-8)/(10y)*(15x^2)/(5x-10)

2. (3x+9)/(x^3)*(2x)/(x^2-8)

3. (x+1)/(x+2)*(2)/(x)

4. (5x^2-5x)/(10) / (6x-6)/(1)

5. (x)/(x+3) / (x-2)/(x+3)

6. (ax+4a)/(a) / (x^2-16)/(x-4)

Answer 1

1st prob:

(4x-8)/(10y)*(15x^2)/(5x-10)

multiply across:

[15x^2(4x-8)]/[10y(5x-10)] = (60x^3-120x^2)/(50xy-100y)

Simplify by dividing top and bottom by 10:

(6x^3-12)/(5xy-10)

2nd prob:

(3x+9)/(x^3)*(2x)/(x^2-8)

multiply across:

[2x(3x+9)]/[x^3(x^2-8)] = (6x^2+18)/(x^5-8x^3)

3rd prob:

(x+1)/(x+2)*(2)/(x)

multiply across:

[2(x+1)]/[x(x+2)] = (2x+2)/(x^2+2x)

4th prob:

(5x^2-5x)/(10) / (6x-6)/(1)

Simplify the first fraction:

(5x^2-5x)/10 = 5(x^2-x)/10 = (x^2-x)/2

(x^2-x)/2 / (6x-6)/1

When dividing 2 fractions flip the second one and then multiply:

(x^2-x)/2 * 1/(6x-6)

Multiply across:

[(x^2-x)(1)]/[2*(6x-6)] = (x^2-x)/(12x-12)

Simplify:

[x(x-1)]/[12(x-1)] = x/12

5th prob:

(x)/(x+3) / (x-2)/(x+3)

Flip second fraction and multiply:

x/(x+3) * (x+3)/(x-2) = [x(x+3)]/[(x+3)(x-2)]

(x+3) cancels from top and bottom in a simplification:

x/(x-2)

6th prob:

(ax+4a)/(a) / (x^2-16)/(x-4)

Simplify both fractions:

(ax+4a)/a = a(x+4)/a = x+4

(x^2-16)/(x-4) = [(x+4)(x-4)]/(x-4) = x+4

Equation becomes:

(x+4) / (x+4) = 1

Hope this helps...b.