Rational Expressions 1

Question 1

simplify: 3x-12 / x²-4x

Answer 1

3(x-4) /x(x-4) = 3/x

Question 2

Simplify: n² +2n -15 /2n +1 X 1/n+5

Answer 2

(n+5)(n-3)/(2n+1)(n+5)

n-3/2n-1

Question 3

Simplify 4n+4/n²-9 divided by 8/2n²+5n-3

Answer 3

4n+4/n²-9 x 2n²+5n-3/8

4(n+1)/(n+3)(n-3) x (2n-1)(n+3)/8

(n+1)(2n-1)/2(n-3)

Question 4

Express as a single fraction

1/x-2 - 3/5x

Answer 4

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

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

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

Question 5

What is key to making a single fraction

Answer 5

finding a suitable denominator

Question 6

simplify 4+ (3/2x+1)

Answer 6

4(2x+1)/2x+1 + 3/2x+1

8x+7/2x+1

Question 7

simplify: x+1/2x-1 + 2/x-5

Answer 7

x²-7/(2x-1)(x-3)

Question 8

simplify: x/(x+2)(x+3) - x²-7x-18/(x+2)(x-1)(x+3)

Answer 8

(x-9)(x+2)/(x+2)(x-1)(x+3)

x-9/(x-1)(x+3)

Question 9

simplify: 1/(1/2 + 1/x)

Answer 9

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

2x/(2+x)