SOLUTION: What is the difference in these two questions and how do I do them? Describe the mathematic process of canceling like factors when working with rational expressions. Demonstrat

Question 570916: What is the difference in these two questions and how do I do them?
Describe the mathematic process of canceling like factors when working with rational expressions. Demonstrate this with an example. And explain in your own words how factoring is used to solve quadratic equations. Demonstrate the process with an example. Please help this is late and I am so lost
Found 2 solutions by richard1234, harsh.9119:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Canceling like factors is similar to canceling common factors in a fraction such as 15/24. Pretty straightforward, as long as you cancel the factors correctly.

Factoring helps solve quadratics, as you don't have to use the quadratic formula. If x^2 + bx + c = 0 factors to (x-p)(x-q) = 0, then right away you know that the roots are p and q. However, not all quadratics factor nicely, and you almost have to "recognize" instantly if a quadratic is factorable (by being able to factor the constant term), otherwise the method is useless.

For example, consider the quadratic . Since 35 = 5*7 and 5+7 = 12, you could factor it like

(check to make sure the coefficients are the same upon expanding). By the zero-product rule, the roots are -5 and -7.

Factoring quadratics with a leading term other than 1 uses a slightly different method; look in your textbook or online for examples.
Answer by harsh.9119(1) (Show Source): You can put this solution on YOUR website!
x^2+12x+35=0
i.e. x^2+7x+5x+35=0
i.e. (x+7)(x+5)=0
i.e. x=-7 && x=-5
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