I am so confused on the steps to solving this problem

Question

 

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

Answer 1

Considering the equation as .

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

Least Common Multiple of 2 and x is 2x.

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

Cross multiplication.

.

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

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Compare the equation, with standard form of quadratic equation .

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Solution, .

.

Solution of is and .

Answer 2

(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.

Answer 3

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.