Answer :
To simplify the expression [tex]\(\frac{3x^2}{12x^3 - 48x^2}\)[/tex], we can follow these steps:
1. Factor the denominator:
Start by factoring out the greatest common factor (GCF) in the denominator. The expression in the denominator is [tex]\(12x^3 - 48x^2\)[/tex].
- The GCF of [tex]\(12x^3\)[/tex] and [tex]\(48x^2\)[/tex] is [tex]\(12x^2\)[/tex].
- Factor out [tex]\(12x^2\)[/tex] from the denominator:
[tex]\[ 12x^3 - 48x^2 = 12x^2(x - 4) \][/tex]
2. Rewrite the expression:
Substitute the factored form back into the expression:
[tex]\[ \frac{3x^2}{12x^2(x - 4)} \][/tex]
3. Simplify by canceling common factors:
In the expression [tex]\(\frac{3x^2}{12x^2(x - 4)}\)[/tex], both the numerator and the denominator have a common factor of [tex]\(3x^2\)[/tex].
- Divide both the numerator and the denominator by [tex]\(3x^2\)[/tex]:
[tex]\[ \frac{3x^2}{12x^2(x - 4)} = \frac{1}{4(x - 4)} \][/tex]
So, the fully simplified expression is [tex]\(\frac{1}{4(x - 4)}\)[/tex].
1. Factor the denominator:
Start by factoring out the greatest common factor (GCF) in the denominator. The expression in the denominator is [tex]\(12x^3 - 48x^2\)[/tex].
- The GCF of [tex]\(12x^3\)[/tex] and [tex]\(48x^2\)[/tex] is [tex]\(12x^2\)[/tex].
- Factor out [tex]\(12x^2\)[/tex] from the denominator:
[tex]\[ 12x^3 - 48x^2 = 12x^2(x - 4) \][/tex]
2. Rewrite the expression:
Substitute the factored form back into the expression:
[tex]\[ \frac{3x^2}{12x^2(x - 4)} \][/tex]
3. Simplify by canceling common factors:
In the expression [tex]\(\frac{3x^2}{12x^2(x - 4)}\)[/tex], both the numerator and the denominator have a common factor of [tex]\(3x^2\)[/tex].
- Divide both the numerator and the denominator by [tex]\(3x^2\)[/tex]:
[tex]\[ \frac{3x^2}{12x^2(x - 4)} = \frac{1}{4(x - 4)} \][/tex]
So, the fully simplified expression is [tex]\(\frac{1}{4(x - 4)}\)[/tex].
