7/(x+1) - 3/2 =6/(3x+3)
Im not sure how to begin, I thought abou clearing the denominators by multiply everything by (x+1)(2)(3x+3) but that didn't work out.
That's what I would do first.
How did it not work out? Show us what you tried and why you think it's wrong...
To solve the equation 7/(x+1) - 3/2 = 6/(3x+3), you can follow these steps:
Step 1: Clear the fractions
Multiply both sides of the equation by the common denominator of all the fractions, which is (x+1)(2)(3x+3). This step will help eliminate the fractions.
By multiplying both sides of the equation by (x+1)(2)(3x+3), we get:
(7/(x+1) - 3/2)(x+1)(2)(3x+3) = (6/(3x+3))(x+1)(2)(3x+3)
Simplifying each side of the equation, we have:
(7(2)(3x+3) - 3(x+1)(2)(3x+3))/(x+1) = 6(2)(x+1)
Step 2: Distribute and simplify
Distribute the terms on both sides of the equation. Simplify wherever possible.
On the left side of the equation, we have:
[(7*2)(3x+3) - (3x+1)(2)(3x+3)]/(x+1)
Simplifying further:
[14(3x+3) - 6(x+1)(3x+3)]/(x+1) = 12(x+1)
Step 3: Combine like terms
Expand and simplify both sides of the equation by distributing and combining like terms.
On the left side of the equation, we have:
[42x+42 - 6(3x+3)(x+1)]/(x+1) = 12x + 12
Simplifying further:
[42x+42 - 6(3x^2+3x+3x+3)]/(x+1) = 12x + 12
[42x+42 - 6(3x^2+6x+3)]/(x+1) = 12x + 12
[42x+42 - 18x^2-36x-18]/(x+1) = 12x + 12
Now, we have an equation without any fractions.
Step 4: Simplify and rearrange
Combine like terms on the left side and simplify the equation.
Starting with the numerator on the left side:
(24x-18x^2 + 24)/ (x+1) = 12x + 12
Combining like terms:
6x - 18x^2 + 6 = 12x + 12
Rearranging the equation:
-18x^2 + 6x -12x - 6 = 12
Step 5: Simplify and solve
Rearrange the equation and solve for x.
Combining like terms:
-18x^2 - 6x - 6 = 12
Now, we are left with a quadratic equation that we can solve using various methods like factoring, completing the square, or the quadratic formula.