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1 I don't know how to do this

Jan 9, 2018

#1
+1

Simplify the following:
5/(1/6 + 1/(x + 1))

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

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

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)

Grouping like terms, x + 1 + 6 = x + (1 + 6):
(5×6 (x + 1))/(x + (1 + 6))

(5×6 (x + 1))/(x + 7)
(30 (x + 1))/(x + 7) = (30x + 30) / (x + 7)

Jan 9, 2018

#1
+1

Simplify the following:
5/(1/6 + 1/(x + 1))

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

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

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)

Grouping like terms, x + 1 + 6 = x + (1 + 6):
(5×6 (x + 1))/(x + (1 + 6))

(5×6 (x + 1))/(x + 7)
(30 (x + 1))/(x + 7) = (30x + 30) / (x + 7)

Guest Jan 9, 2018