Multiplying and Dividing Rational Expressions:
1. 2x^4/x^5 times 6x/x^3 times x/4= 3/x^2
would you tell me please are they correct?
2X^4/X^5 * 6X/X^3 * X/4 =
Multiply all facto in numerator and
denominator:
12X^6 / 4X^8 = 3X^-2 / 1
Multiply numerator and denominator by
x^2:
3 / X^2.
To multiply the rational expressions 2x^4/x^5, 6x/x^3, and x/4, we can follow these steps:
Step 1: Multiply the numerators (top parts) together.
2x^4 * 6x * x = 12x^6.
Step 2: Multiply the denominators (bottom parts) together.
x^5 * x^3 * 4 = 4x^8.
Step 3: Simplify the resulting fraction.
The simplified expression is 12x^6/4x^8.
Step 4: Reduce the fraction by cancelling out common factors.
In this case, we can divide both the numerator and denominator by 4x^6.
12x^6 / 4x^8 = (12/4)(x^6/x^8) = 3/x^2.
Therefore, the product of the rational expressions 2x^4/x^5, 6x/x^3, and x/4 is 3/x^2.
To simplify the given expression (2x^4 / x^5) * (6x / x^3) * (x / 4), you can follow these steps:
Step 1: Combine all the numerators and denominators into a single fraction.
In this case, we have:
(2x^4 * 6x * x) / (x^5 * x^3 * 4)
Step 2: Simplify the numerator.
For the numerator, multiply all the coefficients and add the exponents of similar variables together:
2 * 6 * 1 * x^4 * x * x = 12x^6
Step 3: Simplify the denominator.
For the denominator, multiply all the variables and add the exponents together:
x^5 * x^3 * 4 = 4x^8
Step 4: Combine the simplified numerator and denominator to form the final expression.
The simplified expression is:
12x^6 / 4x^8
Step 5: Further simplify by canceling out common factors.
In this case, both the numerator and denominator have a common factor of 4 and x^6:
(12 / 4) * (x^6 / x^8)
3 * (1 / x^2)
Therefore, the simplified expression is:
3 / x^2