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

$\frac{5x^2+25x+20}{7x}=\frac{5(x^2+5x+4)}{7x}=\frac{5(x+1)(x+4)}{7x}$

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.

$\frac{x^2+2x+1}{x-1}\times\frac{5x^2+15x-20}{7x^2+x}=\frac{(x+1)^2}{x-1}\times\frac{5(x-1)(x+4)_{}}{7x(x+1)}=\frac{x+1}{1}\times\frac{5(x+4)}{7x}=\frac{5(x+1)(x+4)}{7x}$