Simplify fully 3/(2x + 12) - (x - 15)/(x^2 - 2x - 48)

The first step to answering this question is recognising that the denominators should be factorised to find any common factors. Factorising 3/2x+12 gives 3/2(x+6) and factorising (x-15)/(x2-2x-48) gives (x-15)/(x+6)(x-8). The student should then see that the next step would be to put them both over a common denominator so that they can then be subtracted. To do this the first term can be multiplied by (x-8)/(x-8). Then the second term can be multiplied by 2/2. Another way of saying this would be to multiply the top and the bottom of the first fraction by (x-8) and the second one by 2. This then gives 3(x-8)/2(x-8)(x+6) - 2(x-15)/2(x-8)(x+6). The student should then combine the fractions into 1 which is 3(x-8)-2(x-15)/2(x+6)(x-8). The brackets on the top should then be expanded and the expression simplified to (x+6)/2(x+6)(x-8). An easy mistake to make is to forget that the - outside and the - inside create a +. The (x+6) then cancel and the simplified expression is 1/2(x-8)

AC
Answered by Archie C. Maths tutor

4707 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

There are 10 boys and 20 girls in a class. In a class test, the mean score of the boys is 77. The mean score of the girls is 80. What is the mean score of the whole class?


Solve the inequality 6y+5>8?


Solve the simultaneous equations: [4x-y=3] and [6x +2y=1]


Solve the following quadratic equation: x^2 + 3x + 2 = 0


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences