Multiplying and Dividing Rational Expressions:
1. 2x^4/x^5 times 6x/x^3 times x/4= 3/x^2
2X^4 / X^5 * 6X / X^3 * X /4 =
Multiply al factors in numerator and
denominator:
12X^6 / 4X^8 = 3X^-2 / I =
Multiply numerator and denominator by
X^2:
3 / X^2.
To multiply and divide rational expressions, follow these steps:
Step 1: Simplify each rational expression individually.
Let's simplify each expression first:
2x^4/x^5 can be simplified to 2/x.
6x/x^3 can be simplified to 6/x^2.
x/4 is already in simplified form.
So, the given expression becomes: (2/x) * (6/x^2) * (x/4).
Step 2: Multiply the numerators and denominators.
Multiply the numerators: 2 * 6 * x = 12x.
Multiply the denominators: x * x^2 * 4 = 4x^3.
So, the expression becomes: 12x / 4x^3.
Step 3: Simplify the resulting expression.
To simplify the expression, we can divide both the numerator and denominator by the greatest common factor (GCF), which is 4x.
Dividing the numerator by 4x: 12x / 4x = 3.
Dividing the denominator by 4x: 4x^3 / 4x = x^2.
So, the simplified expression is: 3 / x^2.
Therefore, the given expression 2x^4/x^5 * 6x/x^3 * x/4 equals 3/x^2.