We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
279
1
avatar+559 

Write the expression as a simplified rational expression

 Feb 7, 2018

Best Answer 

 #1
avatar
0

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)

 

 Feb 7, 2018
 #1
avatar
0
Best Answer

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)

 

Guest Feb 7, 2018

10 Online Users