Question

Simplify: x^2-10x+9
-----------
x^2+2x-3

Answer 1

x^2-10x+9 = (x-1)(x-9)
x^2+2x-3 = (x-1)(x+3)

Answer 2

x^2-10x+9 x-9
----------- = ---------
x^2+2x-3 x+3

Answer 3

We have
\[\frac{x^2-10x+9}{x^2+2x-3}\]
Let's find the factors of \(x^2-10x+9\)
we have to find factor of 9, such that the sum is -10
-1 and -9 satisfy this
so
\[x^2-10x+9=x^2-9x-x+9\]
we have now
\[x(x-9)-1(x-9)=(x-1)(x-9)\]
so
\[x^2-10x-9=(x-1)(x-9)\]
Now let's find the factor of \(x^2+2x-3=0\)
we have to find the factors 0f -3 such that their sum is 2
3 and -1 satisfy this
we get
\[x^2+2x-3=x^2+3x-x-3=>x(x+3)-1(x+3)\]
we get
\[x^2+2x-3=(x-1)(x+3)\]
We have
\[\frac{x^2-10x+9}{x^2+2x-3}=\frac{\cancel{(x-1)}(x-9)}{\cancel{(x-1)}(x+3)}\]
we get
\[\frac{x-9}{x+3}\]