Mastering Operations with Rational Expressions

What is the first step in simplifying the expression 49x^2y^7z^4 / 35x^8y^3z^12?

• Subtract the exponents of the variables

• Multiply the coefficients

• Add the exponents of the variables

• Divide the coefficients by their GCF

When multiplying rational expressions, why is it beneficial to break down the numbers into smaller factors?

• To simplify the process and avoid large numbers

• To make the numbers larger

• To make the process more complex

• To increase the number of variables

How do you handle the expression 2x / (3x - 6) * (5x - 10) / 20x^2?

• Multiply the numerators and denominators directly

• Factor each part and then cancel common terms

• Subtract the numerators and denominators

• Add the numerators and denominators

What is the least common denominator (LCD) needed to add the fractions 8 / 5x and 3 / 2x^2?

• 2x^2

• 10x^2

• 5x

• 15x^2

How do you simplify the expression 4 / (3 - x) + 7 / (x^2 - 9)?

• Combine the fractions directly

• Subtract the numerators and denominators

• Factor the denominators and find a common denominator

• Multiply the numerators and denominators

What is the result of adding the rational expressions 7y/(5y(y-3)) and 15y/(5y(y-3))?

• 22y/(5y(y-3))

• 7y/(5y) + 15y/(y-3)

• 7y + 15y

• 22y/(y-3)

What is the solution to the equation 5/(2x) = 3/(x-4)?

• x = 20

• x = 4

• x = -20

• x = -4

When simplifying the expression (5x)/(x^2 + 5x + 6) - (2x + 8)/(x^2 + 6x + 8), what is the common denominator?

• x + 4

• x + 2

• x + 3

• x + 2 and x + 3

How do you simplify the complex fraction (x^3/y^2) / (x^2/y^4)?

• x^2/y^3

• x^5/y^6

• x/y^2

• x^2/y

In the equation (x-2)/x = (x-2)/(3x+5), what can you cancel out before solving?

• 3x+5

• x-2

• x

• x+5