Question

Mrs. Cho wrote the following problem on the board.

1 2
x² y
y-2x²
Problem:
Step 1:
Step 2:
2x²
-
x²y x²y
y-2x²
y-2x²
x²y
y-2x²
1O Find a common denominator for the two fractions.
O Divide the numerator and denominator of the first fraction by x2 and y.
• Multiply the numerators, multiply the denominators, and then simplify.
• Multiply the first fraction by the reciprocal of the second fraction.

Answer 1

C) Multiply the numerators, multiply the denominators, and then simplify.

Explanation:

Mrs. Cho wrote the following problem on the board:

`\textsf{Problem:} \quad ((1)/(x^2)-(2)/(y))/(y-2x^2)`

In the first step of her calculations, Mrs Cho rewrote the fractions in the numerator with the common denominator of x²y:

`\textsf{Step 1:} \quad ((y)/(x^2y)-(2x^2)/(x^2y))/(y-2x^2)`

Next, Mrs. Cho combined the fractions in the numerator by subtracting their numerators since they share the same denominator. She also rewrote the denominator as a fraction by dividing it by 1:

`\textsf{Step 2:} \quad ((y-2x^2)/(x^2y))/((y-2x^2)/(1))`

Now, Mrs. Cho applied the rule that dividing by a fraction is equivalent to multiplying by the reciprocal of that fraction:

`\textsf{Step 3:} \quad (y-2x^2)/(x^2y) \cdot (1)/(y-2x^2)`

The next step Mrs. Cho should take is to multiply the numerators, multiply the denominators, and then simplify:

`\textsf{Step 4:} \quad (y-2x^2)/(x^2y(y-2x^2))=(1)/(x^2y)`