simplify the rational expression. State any excluded values.
$$\frac{ x+7 }{ x^2+4x-21 }$$

Question

simplify the rational expression.  State any excluded values.
$$\frac{ x+7 }{ x^2+4x-21 }$$

mathstudent55 · Answer

1. You need to factor the denominator. Then if you have the same factor in the numerator and denominator, divide the numerator and denominator by that factor to cancel it. That's the simplified rational expression.
2. Then set both factors of the denominator equal to zero, solve the two equations. The two values of x are the excluded values.

anonymous · Answer

how do you factor it? I remember something about the lcd but I don't understand how to find it

mathstudent55 · Answer

Set up two sets of parentheses with x on the left side of each:
(x      )(x       )
On the right sides you need two numbers that multiply to -21 and add to 4

anonymous · Answer

would it be -7 and 4

mathstudent55 · Answer

-7 x 4 = -28; That's not -21
-7 + 4 = -3; That's not 4

mathstudent55 · Answer

Remember, the numbers you choose must multiply to -21 and add to 4. Try again.

anonymous · Answer

_7 and 3? it adds to -4 but it needs to be positive, so is there a way to do something in the equation to make it positive because it needs to be negative for -21

mathstudent55 · Answer

Pick 7 and -3
7 x (-3) = -21 and
7 + (-3) = 4
Now you have the two numbers you need. Now fill in the parentheses above.

mathstudent55 · Answer

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