Question

Determine where are each piece below blogs to create a rational expression equivalent to the one shown above

Answer 1

We can write the above expression as

`(5x^2+25x+20)/(7x)=(5(x^2+5x+4))/(7x)=(5(x+1)(x+4))/(7x)`

Now we know that

`x^2+2x+1=(x+1)^2`

And

`7x^2+x=7x(x+1)`

Also for the piece

`5x^2+15x-20=5(x^2+3x-4)=5(x-1)(x+4)`

So we shall use

`5x^2+15-20\text{ }`

And

`x-1\text{ }`

To fill the blanks so that this expression will be similar to the above.

`(x^2+2x+1)/(x-1)*(5x^2+15x-20)/(7x^2+x)=((x+1)^2)/(x-1)*\frac{5(x-1)(x+4)_{}}{7x(x+1)}=(x+1)/(1)*(5(x+4))/(7x)=(5(x+1)(x+4))/(7x)`