How to solve the following for x: (2x+3)/(x-4) - (2x-8)(2x+1) = 1

(The full answer produced answer is annotated working out, but since this text box won't let me submit pictures, I'll do my best to transcribe)First, we gather the two fractions by using a common denominator:[(2x + 3)(2x+1) - (2x-8)(x-4)] / [(x-4)(2x+1)] = 1Then, we can multiply both sides of the equation by the common denominator to avoid having to deal with a fraction:(2x + 3)(2x+1) - (2x-8)(x-4) = (x-4)(2x+1)Expanding out the brackets allows us to gather like terms and simplify:4x^2 + 2x + 6x + 3 - [ 2x^2 - 8x - 8x + 32 ] = 2x^2 + x - 8x - 4with a second line of working:24x - 29 = -7x - 4and a third:31x = 25And so dividing both sides by 31 gives us a final answer of x = 25/31

CF
Answered by Cal F. Maths tutor

3103 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do you solve linear inequalities such as: 5x – 2 > 3x + 11


There are 60 students on a school trip. Each student is either one of, vegan, gluten free, or neither. 27 students were girls. 9 girls were gluten free. 21 students were vegan. 8 boys were vegan. 4 boys were gluten free. How many boys had no dietary's?


Find dy/dx for the following equation: f(x) = x^7 + 7x


Line Q goes through (0,5) and (4,7). Find the equation of Line Q in the form y = mx + c


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning