SOLUTION: For questions 1–2, simplify the rational expression. State any restrictions on the variable help PLEASE? 1.) p^2-4p-32/p+4 2.) q^2+ 11q +24/ q^2 -5q -24

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Question 711193: For questions 1–2, simplify the rational expression. State any restrictions on the variable
help PLEASE?
1.) p^2-4p-32/p+4

2.) q^2+ 11q +24/ q^2 -5q -24
Found 2 solutions by tutor_paul, dfvalen0223:
Answer by tutor_paul(519)   (Show Source): You can put this solution on YOUR website!

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Restriction: p not equal to -4 (zero denominator is undefined)
Factor Numerator:

Cancel out the (p+4) terms and you are left with:

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Factor Numerator:

Factor Denominator:

Note that q=-3 or q=8 give a zero denominator, so those values are not allowed
Cancel out the (q+3) terms and you are left with:

======================
Good Luck,
tutor_paul@yahoo.com
Answer by dfvalen0223(2)   (Show Source): You can put this solution on YOUR website!
1). We can factorize the numerator:


then, we recognize the coefficients, the form of a quadratic equations is:

so:



Now, we can use quadratic equations:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=144 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8, -4. Here's your graph:


roots are p=-4 and p = 8, so:

then:

the restriction on this is: -4 because indetermine the expresion with zero in the denominator and this trend to infinite.
2) Again, We can factorize the numerator:



Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=25 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -3, -8. Here's your graph:

roots are q = -8 and q = -3, so:

too, We can factorize the denominator:



Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=121 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8, -3. Here's your graph:

roots are q = 8 and q = -3, so:

then:

the restriction on this is: 8 because indetermine the expresion with zero in the denominator and this trend to infinite.
Did you understand me?
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