Question

Can anyone please help with this Proof?

Answer 1

The left side is not equal to the right side.

The first term on the left does not simplify to give the first two terms on the right side. The denominator cannot be split into two terms.

Explanation:

This type of question could be given to students learning the basics of Algebra. It simply requires that each term on the left side is simplified and then the left hand side can be compared to the right hand side.

A variety of operations and skills are included for practice.

Let's tackle one term on the left side at a time:

`(160x^5)/(8x^2(4x+5x+x^2)) = (160x^5)/(8x^2(9x+x^2))" "color(white)(www)/(larr"factorise out " x)`

`=(160x^5)/((8x^3)(9+x)) = (20x^2)/color(red)((9+x))` (this term is different on the right)

Now consider the terms in `y`

`14y-(7y+y^3)-3y = 14y-7y-y^3-3y = color(blue)(4y-y^3)`

The term in `z: rarr" "(20z)/(13z-8z) = (20z)/(5z) = 4`

the terms in `q:rarr" "15q-8q^2+3q^2 = color(blue)(15q-5q^2)`

The square brackets simplify to: `color(blue)(6jn+2n^3)`

The last term: `(160j^2)/(40j^2) = 4`

Writing these as one expression gives:

`(20x^2)/(color(red)(9+x))+color(blue)(4y-y^3+15q-5q^2+6jn+2n^3+8`

which is not the same as the right hand side

`(20x^2)/(color(red)(9)) + color(red)(20x)+color(blue)(4y-y^3+15q-5q^2+6jn+2n^3+8`