If I am dividing the following:
x^2+3x over x^2+2x-3 by x over x+1.. i know to do the recip. of x over x+1 and get the foll.
x^2 + 3x over x^2 + 2x -3 times x+1 over x... now
(x^2+3x)(x+1) over
(x^2+2x-3)(x)
now
x(x+2)(x+1)
x(x+2)(x-1)
the x+2 over x+2 = 1
so wouldn't the value be 1?
x^2+3x over x^2+2x-3 by x over x+1
= (x^2+3x)/(x^2+2x-3)*(x)/(x+1)
= x(x+3)/[(x+3)(x-1)*x?(x+1)
= x/(x-1)*x/(x+1)
= x^2/(x^1 - 1)
To solve the division problem:
1. Simplify both the numerator and denominator separately:
- Factor the numerator, x^2 + 3x:
x^2 + 3x = x(x + 3)
- Factor the denominator, x^2 + 2x - 3:
x^2 + 2x - 3 = (x + 3)(x - 1)
2. Rewrite the division problem with the simplified expressions:
(x(x + 3)) / ((x + 3)(x - 1)) * (x + 1) / x
3. Cancel out any common factors between the numerator and denominator:
(x ~cancel~ (x + 3)) / ((x + 3)(x - 1)) * (x + 1) / x
Note: The x + 3 in the numerator and denominator cancels out.
4. Simplify the expression further:
1 / (x - 1) * (x + 1) / x
5. Multiply the factors:
(1 * (x + 1)) / ((x - 1) * x)
6. Distribute and simplify:
(x + 1) / (x^2 - x)
Therefore, the expression after simplifying the division is (x + 1) / (x^2 - x).