Question

Rewrite in simplest terms: 2(-4c-3) ÷ 6(10c - 5)

a) (4c + 3)/(15c - 5)
b) (2c + 3)/(5c - 5)
c) (2c - 3)/(5c + 5)
d) (4c - 3)/(15c + 5)

Answer 1

To simplify the expression 2(-4c-3) ÷ 6(10c - 5), we distribute the coefficients in the numerator and the denominator, then divide both by their greatest common factors. The simplified expression is (4c + 3)/(15c - 5), which corresponds to option a).

Step-by-step explanation:

To solve the given expression 2(-4c-3) ÷ 6(10c - 5), we need to simplify both the numerator and the denominator before dividing.

Firstly, distribute the 2 in the numerator:

2(-4c) + 2(-3) = -8c - 6

Then, distribute 6 in the denominator:

6(10c) - 6(5) = 60c - 30

Now our division becomes:

(-8c - 6) / (60c - 30)

To simplify further, divide both numerator and denominator by the common factor of 2:

(-4c - 3) / (30c - 15)

And then, divide by the common factor of -1 to get rid of negative symbol in numerator:

(4c + 3) / (-30c + 15)

Finally, divide both by the common factor of 15:

(4c + 3)/(15c - 5)

This matches option a), so the expression simplified in the simplest terms is (4c + 3)/(15c - 5).