Question

Simplify: (x^2+3x+2)/(5x^2+10x) x 15x/(x^2+1)
[A2 maths, AQA core 4]

Answer 1

I would factor the top and bottom of the first fraction

Answer 2

Okay, having factorised and simplified it, I now have:
3(x+1) / (x^2-1) but the answer states it should be 3/(x-1)

Answer 3

you can factor (x^2-1) (a difference of squares)

Answer 4

***15x/(x^2+1)***
I assume this is a typo and you mean 15x/(x^2-1) ?

Answer 5

Yes sorry

Answer 6

so factor (x^2-1) into (x-1)(x+1)

(it's good to recognize the difference of squares)
\[ (a^2 - b^2) = (a+b)(a-b) \]

Answer 7

Okay I see, I had it in mind that you had to half the value of 'b' when you carry out DOTS

Answer 8

the last step is make a note of any excluded values (x values that would cause a divide by zero in the original equation)

***you had to half the value of b ****
You might be thinking of "completing the square"
\[(x^2 +2bx+b^2) = (x+b)^2 \]
example: \( (x^2 +2x+1^2) = (x+1)^2 \)

Answer 9

difference of squares is easy, as long as you can recognize that you have two squares
for numbers, you should now the squares 1,4, 9, 16 , etc
also
\[ x^4 = x^2 \cdot x^2 =\left(x^2\right)^2 \]
i.e. if the exponent is even, you can write it as a square