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Simplify the expression: (x^2 + x - 6)/(3x^2 + 9x)

Factorise the numerator: x^2 + x - 6 = (x+3)(x-2) Factorise the denominator: 3x^2 + 9x = 3x(x+3) Cancel '(x+3)' Answer: (x-2)/3x
RD
Answered by Richard D. • Maths tutor
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By 1547 to what extent can Henry VIII's religious settlement be considered 'Catholicism without the Pope'?

It can be argued that to a large extent, by 1540 that the religious society in England can be considered Catholicism without the Pope. Initially when the reformation began Henry pushed for a very protestant ...
AS
Answered by Alice S. • History tutor
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Prove ∑r^3 = 1/4 n^2(n+1)^2

Proof by induction Base Case when n=1 LHS = 1^3=1 RHS= 1/4(1^2)(1+1)^2=1/4(1)(2^2)=1/4(4) Assume true for n=k so ∑r^3= 1/4k^2(k+1)^2 For n=k+1 ∑r^3 = ∑k terms + (k+1)^3 = 1/4(k^2)(k+1)^2 + (k+1)^3 = 1/4(k^2)...
JO
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sin(x)/(cos(x)+1) + cos(x)/(sin(x)+1) = 1

sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1 (sin^2(x) + cos^2(x) =1) Therefore; 1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1 Cancelling out on both sides cos(x)sin(x) =...
JO
Answered by James O. • Maths tutor
4469 Views

Which is 'the most important' in the US - the Senate or the House?

Whilst the US Constitution makes no reference to which is more important than the other, the Senate can be seen as more important for a number of reasons. Senators are elected every six years, as opposed to ...
JW
Answered by Jake W. • Politics tutor
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