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Simplify the algebraic expression: (3x^2-7x-6)/(x^2-6x+9)

We start by noticing that both the numerator and denominator are expressions which can be factorised into brackets. Starting with the numerator, we multiply the coefficient of x^2 and the constant term toget...
EG
Answered by Emily G. • Maths tutor
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Why is bacteria in school labs incubated at 25°C or lower?

Bacteria resides virtually everywhere around (and within) us. In schools and university conditions, bacteria cultures are incubated at 25°C or lower to reduce the chances of growing harmful pathogens which c...
EP
Answered by Ekaterina P. • Biology tutor
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Solve the simultaneous equations: 3x − y = 23 2x + 3y = 8

Write the 2 equations above each other: 3x-y=23 2x+3y=8First we want to remove the y terms to be able to find out x, so multiply the top equation by 3 9x-3y=69 2x+3y=8Now that we have -3y on the top and -3y ...
JB
Answered by Jessica B. • Maths tutor
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Differentiate y = x*cos(2x)

cos(2x) - 2x*sin(2x)
PM
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n is an integer greater than 1. Prove algebraically that n^2 – 2 – (n – 2)^2 is always an even number.

1) Expand the brackets: (n-2) 2 = (n-2)(n-2) = n 2 - 2n - 2n +4 = n 2 - 4n + 4 2) Substitute this into the original expression: n 2 - 2 - (n 2 - 4n +4) = n 2 - 2 - n 2 + 4n - 4 = 4n - 6 3) Reduce this: 4n - ...
JM
Answered by James M. • Maths tutor
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