Question

help plz..question 1. Are 2x+4/3x+6 and 2/3 equivalent expressions? Using complete sentences explain why or why not...

question 2..Using complete sentences, explain each step in simplifying the ratio and provide the simplified form.x^2+8x/x^2+10x+16

Answer 1

well the expression can be written as

\[\frac{2x + 4}{3x + 6}\]

when factorised you get

\[\frac{2(x +2)}{3(x + 2)}\]

you need to decide if there is a common factor that can be removed to simplify the expression.

If there is a common factor what's left?

Answer 2

for question 2.

Factorise the numerator and denominator.... there will be a common factor that can be removed,

Answer 3

question 1.cancel out +2??

Answer 4

why not just cancel (x +2)

its in the numerator and denominator

Answer 5

question 2 will be...x^2 + 8x)/(x^2 + 10x +16)

x(x + 8)/(x + 8)(x + 2) get this by factoring each expression
the (x + 8)/(x + 8) = 1 so they cancel each other and the expression simplifies to:

x/(x + 2)

you can prove to yourself that the factors are correct by multiplying the terms again to get the original expression

Answer 6

thats correct.

to do the next part

I'd show

\[\frac{(x + 8)}{x + 8} \times \frac{x}{x+ 2} = \frac{x^2 + x8}{x^2 + 10x + 16}\]

Answer 7

k thanks