Express 3/2x+3 – 1/2x-3 + 6/4x^2-9 as a single fraction in its simplest form.
First it is necessary to notice that 4x^2-9 can be written as (2x-3)(2x+3). To solve this question, you first have to write all the fractions in terms of their lowest common denominator. In this case that is (2x+3)(2x-3). Therefore you have to multiply 3/2x+3 by 2x-3/2x-3 and 1/2x-3 by 2x+3/2x+3. This will leave you with 3(2x-3)-1(2x+3)+6/(2x-3)(2x+3). If you multiply this out you are left with 4x-6/(2x-3)(2x+3). 4x-6 can be rewritten as 2(2x-3), and therefore the 2x-3s cancel out leaving 2/2x+3 which is the final answer.
DS
Related Maths A Level answers
All answers ▸whats the integral of x.e^x wrt x
Express 4x/(x^2-9)-2/(x+3) as a single fraction in its simplest form
A stone was thrown with velocity 20m/s at an angle of 30 degrees from a height h. The stone moves under gravity freely and reaches the floor 5s after thrown. a) Find H, b)the horizontal distance covered
The quadratic equation (k+1)x^2 + (5k-3)x + 3k = 0 has equal roots, find the possible values of the real number k.