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
Related Maths GCSE answers
All answers ▸Solve the pair of simultaneous equations {4x + y = 5, 3x - y = 2} using i) a graph and ii) an algebraic method
Bob buys a car for £120 after it is reduced by 20% in the sale. What was the original price of the car?
Amber earns £7 for each hour she works from Monday to Friday. She earns £10 for each hour she works on Saturday. One week Amber worked for 4 hours on Saturday. That week she earned a total of £180. How many hours did Amber work that week?
Make x the subject of the equation. 7xy+6 = 18x+3y+7