Multiply. x^2/x+5 times x^2+4x-5/x^2-4x?

x^2/(x+5) [ (x+5)(x-1)] =x^2(x-1)
x^2(x-1)/x(x-4)=x(x-1)/(x-4)
God bless you.

[x^2/(x+5)] x [(x^2+4x-5)/(x^2-4x)]
=[x^2/(x+5)] x [(x+5)(x-1)/(x^2-4x)]

(x+5) cancels each other
=x^2 x {(x-1)/[x(x-4)]}
=x X (x-1)/(x-4)
=x(x-1)/(x-4)

i'm presuming that that is... (2x - 3) / (x + 5) - [ (x² - 4x) / (x² + 8x + 15) ] First, you opt to element the 2d fraction to confirm if something can cancel out. (2x - 3) / (x + 5) - [ x(x - 4) ] / [ (x + 3)(x + 5) ] no longer something cancels out yet. So now we would decide to subtract fractions. first element we do is to make the two denominators the comparable. lcd is (x + 3)(x + 5), so multiply the two halves of the 1st fraction by ability of (x + 3) to make the two denominators the comparable ... [ (x + 3)(2x - 3) ] / [ (x + 3)(x + 5) ] - [ x(x - 4) ] / [ (x + 3)(x + 5) ] Now we are able to subtract the two numerators: [ (x + 3)(2x - 3) - x(x - 4) ] / [(x + 3)(x + 5)] Now, simplify the numerator and refactor if that is attainable. (2x² - 3x + 6x + 9 - x² + 4x) / [(x + 3)(x + 5)] (x² + 7x + 9) / [(x + 3)(x + 5)] The numerator won't be able to element out, so we are able to strengthen the denominator and bypass away that as our answer: (x² + 7x + 9) / (x² + 8x + 15)

(x^2)/(x + 5) * (x^2 + 4x - 5)/(x^2 - 4x)
= (x^2)/(x + 5) * (x^2 + 5x - x - 5)/[x(x - 4)]
= (x^2)/(x + 5) * [(x^2 + 5x) - (x + 5)]/[x(x - 4)]
= (x^2)/(x + 5) * [x(x + 5) - 1(x + 5)]/[x(x - 4)]
= (x^2)/(x + 5) * [(x + 5)(x - 1)]/[x(x - 4)]
= x^2 * (x - 1)/[x(x - 4)]
= x * (x - 1)/(x - 4)
= [x(x - 1)]/(x - 4)

ok this is pretty simple.
1st factor out (x^2 + 4x - 5), you get (x+5)(x-1)
2nd factor out a x from x^2 - 4x, you get x(x-4)
3rd replace them as following

(x)(x) [(x+5)(x-1)]
----------------------
(x+5) [x(x-4)]

4th cancel out common term from both sides, so x from numerator(top left) cancels out x from denominator(bottom right) and (x+5) cancels out from top and bottom.

so now you are left with

x(x-1)
-------- Final answer.
(x-4)

** Note:- In rational multiplication, you multiply top together divided by bottom multiplied together.Whenever you working with polynomials, factor out the common terms, chances are it will get canceled.

(x^2)/(x+5)*(x^2+4x-5)/(x^2-4x)

(x*x)/(x+5)*( (x+5)(x-1) )/( x*(x-4))
one of the lone "x" cancels out, (x+5) cancels out.

(x^2-x)/(x-4)

(x^4+4x^3-5x^2)/(x^3+x^2-20x)