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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 squared root of 2 is an irrational number

Let's start by assuming that the squared root of 2 is a rational number and will prove it is irrational by contradiction.If srqt(2) is rational then it can be represented by an irreducible fraction. Let this...
RN
Answered by Raul N. • 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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prove that lnx differentiated is 1/x

let y = lnx therefore e^y = x then differentiating both sides we get: dy/dx (e^y) = 1 dy/dx = 1/(e^y) and as e^y = x dy/dx = 1/x when y = lnx
Answered by • Maths tutor
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Find the coordinates of the point of intersection of the lines 2x + 5y = 5 and x − 2y = 4.

Rearrange both equations to make y the subject:2x + 5y = 5 rearranges to y = -2x/5 + 1 and x - 2y = 4 rearranges to y = x/2 - 2Equate both the rearranged equations and solve for x:-2x/5 + 1 = x/2 - 2x = 10/3...
EO
Answered by Ethan O. • Maths tutor
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