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Solve 6/(x-3) + x/(x+4) = 1

(6(x+4) + x(x-3) )/ ((x-3)(x+4)) = 1 obtain a common denominator and write as one fraction. (6x+24+x²-3x ) /( x²-3x+4x-12) = 1 multiply out the brackets. (x²+3x+24)/ (x

Answered by Jana R. • Maths tutor

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Solve these simultaneous equations: 2x + 3y = 19 and x + 4y = 17.

By multiplying everything in equation 2 by 2, you get 2x + 8y = 34. If you then subtract equation 1 from this you get 5y = 15. Thus y = 3, going back to equation two, and subbing y back in, x + 12 = 17, t...

Answered by James H. • Maths tutor

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Find the equation of the straight line that is tangent to the curve 2x^2 - 5x - 3 =0 when x = 3.

First differentiate 2x² - 5x - 3 to get 4x -5. At x = 3, the gradient of the tangent must be 7, and we know it goes through (3, 0) Plug the values into y = mx + c to get the equation of the lin...

Answered by Sarah L. • Maths tutor

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Prove that the square of an odd number is always 1 more than a multiple of 4

In order to prove this we can write a general expression of an odd number in terms of n, e.g - 2n+1Square this 'odd number': (2n+1)^2, therefore you can write it as (2n+1)(2n+1), then expand (multiply out...

Answered by Ben H. • Maths tutor

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(This was taken from a GCSE past paper)A bag of 24 spoons costs £19.95. A box of 18 forks costs £15.55. Bags and boxes cannot be split. Gregor decides to buy the same number of spoons as forks. He places an order to buy the smallest number of each

We are finding the Highest common multiple (HCM) of two numbers in this question. To find the HCM, first the prime factors have to be found, this means writing each number as a multiplication of the small...

Answered by Tom N. • Maths tutor

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