3/x=5/x-7
Let's begin by highlighting all of the different factors in the denominators. This will help us find the least common denominator (LCD).
3/x=5/x-7
We will solve the equation by multiplying each side by the LCD to clear denominators.
We see that x = -10.5. Finally, we will check if this solution is extraneous. To do this, let's recall the least common denominator by which we have multiplied our equation.
x (x-7)
Notice that the above expression equals 0 only for x = 0 and for x = 7. Since this is the least common denominator, the original expression is undefined only for those values of x. Therefore, as our solution is not equal to any of these numbers, the solution is not extraneous.
b We want to solve the given equation.
2x+3/4 - x-7/6 = 2x-3/12Let's first factor the denominators and highlight all of the different factors. This will help us find the least common denominator (LCD).
2x+3/4 - x-7/6 = 2x-3/12
⇓
2x+3/2 * 2 - x-7/2 * 3 = 2x-3/2 * 2* 3
The least common denominator is 2 * 2* 3 = 12. We will solve the equation by multiplying each side by the LCD to clear denominators.
