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Solve (2x^2 - 3x - 14)/(x^2 + 6x + 8) = -6/(x+3).

LHS: Factorise numerator and denominator, which gives:((2x - 7)(x + 2))/((x + 2)(x + 4))Cancel out (x + 2), gives:(2x - 7)/(x + 4)Multiply both sides by (x + 4)(x + 3) to cancel the denominators, gives:(2x -...
JL
Answered by Joseph L. • Maths tutor
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Prove that the square of an odd number is always 1 more than a multiple of 4

Let n be any whole number. Any odd number can be written as 2n+1. Any odd number squared is therefore (2n+2) 2 =2n 2n+2 2n+1=4n 2 +4n+1=4(n 2 +n)+1. n 2 +n is a whole number, so 4(n 2 +1) is a multiple of 4....
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A linear sequence starts with: a + 2b ; a + 6b ; a + 10b etc. The 2nd term has value 8. The 5th term has value 44. Work out the values of a and b.

We know that the 2nd term has a value of 8. Thus a + 6b = 8;What is more, we also know that the 5th term has a value of 44. We also know that the next element in the sequence increases by 4b when compared to...
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Share £200 in the ratio 2:3

200/(2+3) = 4040 2 = 8040 3 = 120£80:£120
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3^2 + 4^2 = x^2. Find x

By Pythagoras’s theorem, a 2 +b 2 = c 2 . So x 2 = 9+16=25 and so by finding the square root of 25, x=5
LM
Answered by Luke M. • Maths tutor
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