Combine the following fractions and express in fully reduced form. start fraction, 7, divided by, 6, x, end fraction, plus, start fraction, 1, divided by, x, end fraction 6x 7 ​ + x 1 ​

1 answer

To combine the fractions, we need to find a common denominator.

The common denominator of 6x and x is 6x.

Thus, the fractions become:
(7/x)(6x) + (1)(6) / (6x)

Expanding the fractions gives:
42 / 6x + 6 / 6x

Combining the fractions gives:
(42 + 6) / 6x = 48 / 6x

Now, we can simplify this fraction by dividing both the numerator and denominator by 6:
48 ÷ 6 = 8
6x ÷ 6 = x

Therefore, the fully reduced form is:
8 / x