Express 2(x-1)/(x^2-2x-3) - 1/(x-3) as a fraction in its simplest form.
The answer is 1/(x+1)I began by factorising the denominator of the first fraction:2(x-1)/(x^2-2x-3) - 1/(x-3) = 2(x-1)/(x-3)(x+1) - 1/(x-3) Next, I multiplied both the numerator and the denominator of the second fraction by (x+1) to get a common denominator:2(x-1)/(x-3)(x+1) - 1/(x-3) = 2(x-1)/(x-3)(x+1) - (x+1)/(x-3)(x+1) With this common denominator, I could then expand the brackets on the numerators and add/subtract accordingly:2(x-1)/(x-3)(x+1) - (x+1)/(x-3)(x+1) = (2x-2-x-1)/(x-3)(x+1) = (x-3)/(x-3)(x+1) The last step I did was dividing the common factor of (x-3) from the numerator and denominator to give:(x-3)/(x-3)(x+1) = 1/(x+1)
DR
Related Maths A Level answers
All answers ▸What is the integral of x sin(x) dx?
The quadratic equation 2x^2 + 8x + 1 = 0 has roots a and b. Write down the value of a + b, a*b and a^2 + b^2.
Integrate ln(x) by parts then differentiate to prove the result is correct
Find the gradient of the tangent to the line y=(x-2)^2 at the point that it intercepts the y-axis