To solve the equation, we need to first simplify the left side of the equation by finding a common denominator for the fractions:
(x^2 - 4)/3 - (6 - x)/2
To find a common denominator, we multiply the denominator of the first fraction by 2 and the denominator of the second fraction by 3:
= (2(x^2 - 4) - 3(6 - x))/6= (2x^2 - 8 - 18 + 3x)/6= (2x^2 + 3x - 26)/6
Now we set this expression equal to 3 and solve for x:
(2x^2 + 3x - 26)/6 = 32x^2 + 3x - 26 = 182x^2 + 3x - 44 = 0
Now we solve this quadratic equation by factoring or using the quadratic formula:
The factors of -88 that add up to +3 are +11 and -8:
(2x + 11)(x - 4) = 02x + 11 = 0 or x - 4 = 02x = -11 or x = 4x = -11/2 or x = 4
Therefore, the solutions to the equation are x = -11/2 or x = 4.
To solve the equation, we need to first simplify the left side of the equation by finding a common denominator for the fractions:
(x^2 - 4)/3 - (6 - x)/2
To find a common denominator, we multiply the denominator of the first fraction by 2 and the denominator of the second fraction by 3:
= (2(x^2 - 4) - 3(6 - x))/6
= (2x^2 - 8 - 18 + 3x)/6
= (2x^2 + 3x - 26)/6
Now we set this expression equal to 3 and solve for x:
(2x^2 + 3x - 26)/6 = 3
2x^2 + 3x - 26 = 18
2x^2 + 3x - 44 = 0
Now we solve this quadratic equation by factoring or using the quadratic formula:
The factors of -88 that add up to +3 are +11 and -8:
(2x + 11)(x - 4) = 0
2x + 11 = 0 or x - 4 = 0
2x = -11 or x = 4
x = -11/2 or x = 4
Therefore, the solutions to the equation are x = -11/2 or x = 4.