Write the expression as a simplified rational expression

Simplify the following:

5/(1/6 + 1/(x + 1))

　

Put the fractions in 1/(x + 1) + 1/6 over a common denominator.

Put each term in 1/(x + 1) + 1/6 over the common denominator 6 (x + 1): 1/(x + 1) + 1/6 = (x + 1)/(6 (x + 1)) + 6/(6 (x + 1)):

5/((x + 1)/(6 (x + 1)) + 6/(6 (x + 1)))

　

Combine (x + 1)/(6 (x + 1)) + 6/(6 (x + 1)) into a single fraction.

(x + 1)/(6 (x + 1)) + 6/(6 (x + 1)) = ((x + 1) + 6)/(6 (x + 1)):

5/((x + 1 + 6)/(6 (x + 1)))

　

Write 5/((x + 1 + 6)/(6 (x + 1))) as a single fraction.

Multiply the numerator of 5/((x + 1 + 6)/(6 (x + 1))) by the reciprocal of the denominator. 5/((x + 1 + 6)/(6 (x + 1))) = (5×6 (x + 1))/(x + 1 + 6):

(5×6 (x + 1))/(x + 1 + 6)

　

Group like terms in x + 1 + 6.

Grouping like terms, x + 1 + 6 = x + (1 + 6):

(5×6 (x + 1))/(x + (1 + 6))

　

Evaluate 1 + 6.

1 + 6 = 7:

(5×6 (x + 1))/(x + 7)

　

Multiply 5 and 6 together.

5×6 = 30:

(30 (x + 1))/(x + 7) =(30x + 30) / (x + 7)