Posted by Joel on October 26, 2002 at 15:15:18:
In Reply to: Homework help posted by Billy on October 26, 2002 at 14:41:15:
Here are some clues to get you started. Now give them a try, & if you get stuck, show what you tried.
: I got some problems i need help with please.
: Simplify each rational expression
: 1/5 over 5/18 1/5/5/18
remember that dividing by X is the same as multiplying by 1/X; or dividing by a/b is the same as multiplying by b/a
: multiply
: x^2+10x+21/x^2+15x+56 times x^2+8x/x^2+9x+18
When you write polynomials like this on one line, get used to putting them in parentheses. Otherwise your readers will not know what is being divided (or multiplied) by what, and in what order. So here you should write:
[(x^2+10x+21)/(x^2+15x+56)] * [(x^2+8x)/(x^2+9x+18)]
Now, before you try doing all that division and multiplication, factor each expression and see what you can cancel out.
: use the quotient rule to simplify
: square root of 144x^4 over the square root of 6x
the rule to use here is (sqrt(a))/(sqrt(b)) = sqrt(a/b). You can take those two square root expressions & combine them into one square root
(the square root of a fraction) and then you can simplify the fraction.
: find all numbers that must be excluded from the domain of each expression.
: x^3+4x^4 over x^2+36
(x^3+4x^4)/(x^2+36)
The domain of the expression is the set of all values from which the values of the variable can be chosen. You know of course that division by zero is not allowed. When an expression is in the form of a fraction, with a variable in the denominator, you must exclude from the domain any values of the variable (x in this example), that would cause the denominator to be zero. So, what values of x would cause (x^2 + 36) to equal 0? (Another hint: factor it before you answer that question.)
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: thanks