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I am so confused on the steps to solving this problem

+2 votes

 

How would you solve (3/x+1)-(1/2)=(1/3x+3)?

asked Feb 2, 2013 in ALGEBRA 1 by anonymous Apprentice

3 Answers

0 votes
 
Best answer

Considering the equation as image.

Fractions with different denominators can not be added. So, write the equation with common denominator.

Left side, Least Common Multiple of x and 1 is x and right side Least Common Multiple of 3 and 1 is 3

image

Least Common Multiple of 2 and x is 2x.

image

Apply distributive property : a(b + c) = ab + ac.

image

image

Cross multiplication.

image

image

image

image.

image, is a quadratic, so, use quadratic formula to find the roots of the related quadratic equation.

image.

Compare the equation, with standard form of quadratic equation image.

image.

Solution, image.

image

image

image

image.

Solution of image is image and image.

answered Jun 27, 2014 by lilly Expert
selected Jul 2, 2014 by casacop
+2 votes

(3/x) + 1 - 1/2 = (1/3x) + 3.

(3/x) + 1/2 = (1/3x) + 3.

Rewrite the expression with common denominator.

(6 + x) / 2x = (1 + 9x) / 3x.

Cross multiplication.

3x(6 + x) = 2x(1 + 9x)

Distribute terms using distributive property:  a( b + c) = ab + ac.

(3x)6 + (3x)x = (2x)1 + (2x)(9x)

18x + 3x2 = 2x + 18x2

Subtract 18x + 3x2 from each side.

15x2 - 16x = 0

Take out common term.

x(15x - 16) = 0

x = 0 or 15x - 16 = 0

Now take 15x - 16 = 0

Add 16 to each side.

15x = 16

Divide each side by 15.

x = 16/15.

answered Feb 2, 2013 by richardson Scholar
+2 votes

3/(x+1) - (1/2) = 1/(3x+3)

Rewrite the expression with common denominator.

[6 - (x + 1)] / 2(x + 1) = 1 / 3(x + 1)

Multiply each side by (x + 1).

(6 - x - 1) / 2 = 1 / 3

(5 - x) / 2 = (1/3)

Cross multiplication.

3(5 - x) = 2

Distribute terms using distributive property:  a( b + c) = ab + ac.

15 - 3x = 2

Subtract 15 from each side.

- 3x = - 13

Divide each side by '-3'.

x = 13/3.

answered Feb 2, 2013 by richardson Scholar

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