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Separate (9x^2 + 8x + 10)/(x^2 + 1)(x + 2) into partial fractions.

First, we find the form of the two fractions we're going to get. As one denominator has a power of 2, and the other a power of 1, our answer will be of the form: [(Ax+B)/(x²+1)] + [C/(x+2)]. If...

Answered by Laura U. • Maths tutor

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Emily bought 3 books and 2 apples, and she spent £19, while her brother, John, spent £15 on 1 book and 5 apples. What is the cost of one book and one apple?

First we assign, for example, that x = cost of 1 book, and y = cost of 1 apple. Then we make these into simultaneous equations, such as: 3x+2y=19 (eqn. 1) and x+5y=15 (eqn. 2). Now multiply eqn. 2 to get ...

Answered by Laura U. • Maths tutor

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Let f ( x ) = 15 /x and g ( x ) = 2 x − 5 Find fg(4), gf(-30) and give the expression for gf(x)

Key here is the order of operation.g(4) =2x4 - 5=8-5=3fg(4) = f(3)=15/3=5gf(-30)f(-30)=15/-30=-1/2gf(-30)=g(-1/2)=2x-1/2 -5=-1-5=-6gf(x)f(x)=15/xg(15/x)=2*15/x -5=30/x -5

Answered by Eddie M. • Maths tutor

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4^x - 2^x+1 - 15 = 0

x = log5/log2

Answered by Narhen E. • Maths tutor

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Solve the Simultaneous equations. 3x+5y=22 4x-5y=6

3x+5y=224x-5y=6Our first task is to cancel out one of the variables. So you see that both y variables have a 5 before them. As one has -5 and the other has +5 you can add both simultaneous equations toget...

Answered by Chris L. • Maths tutor

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