Simplifying expressions with fractions

[andyleija]

The instructions say, "Find f(x)/g(x). Simplify your answer." I'm not sure if I'm supposed to be able to simplify these questions any further. Any help is appreciated. Thanks in advance.

1) f(x) = 3x, g(x) = x + 2
3x/x + 2

2) f(x) = x^2 + 1, g(x) = x -2
x^2 + 1/x - 2

3) f(x) = x - 2, g(x) x^2 + x - 4
x - 2/x^2 + x - 4

4) f(x) = (2x)^(1/2), g(x) = 2 sqrt(2) x^(1/3)
(2x)^(1/2)/2 sqrt(2) x^(1/3)

 

[Deleted member 4993]

Re: Simplifying expressions with factors

The instructions say, "Find f(x)/g(x). Simplify your answer." I'm not sure if I'm supposed to be able to simplify these questions any further. Any help is appreciated. Thanks in advance.

1) f(x) = 3x, g(x) = x + 2
3x/x + 2

2) f(x) = x^2 + 1, g(x) = x -2
x^2 + 1/x - 2

3) f(x) = x - 2, g(x) x^2 + x - 4
x - 2/x^2 + x - 4

4) f(x) = (2x)^(1/2), g(x) = 2 sqrt(2) x^(1/3)
(2x)^(1/2)/2 sqrt(2) x^(1/3)

Are you supposed to find expression for:

\(\displaystyle \frac{f(x)}{g(x)} \, = \, ??\)

 

[andyleija]

Re: Simplifying expressions with factors

The instructions say, "Find f(x)/g(x). Simplify your answer." I'm not sure if I'm supposed to be able to simplify these questions any further. Any help is appreciated. Thanks in advance.

1) f(x) = 3x, g(x) = x + 2
3x/x + 2

2) f(x) = x^2 + 1, g(x) = x -2
x^2 + 1/x - 2

3) f(x) = x - 2, g(x) x^2 + x - 4
x - 2/x^2 + x - 4

4) f(x) = (2x)^(1/2), g(x) = 2 sqrt(2) x^(1/3)
(2x)^(1/2)/2 sqrt(2) x^(1/3)

Are you supposed to find expression for:

\(\displaystyle \frac{f(x)}{g(x)} \, = \, ??\)

Yes, and simplify it.

 

[mmm4444bot]

3x/(x + 2)

(x^2 + 1)/(x - 2)

(x - 2)/(x^2 + x - 4)

[(2x)^(1/2)]/[2 sqrt(2) x^(1/3)]

Please type grouping symbols when numerators or denominators contain more than one term; otherwise, the ratios are not clear.

For example, without grouping symbols, 3x/x + 2 actually means that 2 is being added to the ratio 3x/x.

The expression 3x/(x + 2) cannot be simplified.

The expression (x^2 + 1)/(x - 2) cannot be simplified because x - 2 is not a factor of x^2 + 1.

IF the numerator were to be x^2 - 1 AND the denominator were to be x - 1, THEN a simplification could be done because x - 1 is a factor of x^2 - 1:

(x + 1)(x - 1)/(x - 1) = x + 1

The expression (x - 2)/(x^2 + x - 4) cannot be simplified because x - 2 is not a factor of x^2 + x + 4.

IF the denominator were to be x^2 - 4, THEN a simplification could be done because x - 2 is a factor of x^2 - 4:

(x - 2)/[(x + 2)(x - 2)] = 1/(x + 2)

See how these simplifications work? You factor numerator and denominator, and then cancel common factors.

The expression [(2x)^(1/2)]/[2 sqrt(2) x^(1/3)] can be simplified because there is a common factor in the numerator and denominator that cancels and there is a power of x in both the numerator and denominator.

Do you see the cancellation?

If not, then rewrite the given expression using radical signs instead of exponents, and stare at that.

After you cancel the common factor, go back to exponential form, and use the following rule of exponents.

x^n/x^m = x^(n - m)

The simplified expression has the form Ax^B, where A and B are rational numbers.