2006-10-11 09:07:58 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Sure we do.
For linear equations, it simply does not have much point - you'd just end up with that variable in the denominator - how would you go about solving that?
But, if you are solving a higher degree equation, it can help, or even be the only way to solve it analytically.
For example: x^3 - 2x^2 + x = 0.
Solving a general cubic equation could get tricky, but dividing both parts by x, you can easily find the two solutions (0 and 1) for this case.
One thing to remember, as pointed out above is that x=0 could be a solution - you need to check for it directly before dividing.
Sometimes, it can even be useful to divide an equation by an expression, not just a variable.
For example x^3-3x^2-x+3=0. Dividing it by x does not help anything.
But divide it by x-3 - and you'll see right away that the three solutions here are -1, 1 and 3
2006-10-11 09:19:40 · answer #1 · answered by n0body 4 · 0⤊ 0⤋
Because it can eliminate solutions where the variable is equal to zero. Suppose you have the equation x^2 = x. You can rewrite that as x^2 - x = 0, and factor it as x(x - 1) = 0, so x = 0 or x - 1 = 0 ==> x = 1. But if you start by dividing by x instead, you just get x = 1, losing your solution of x = 0.
2006-10-11 09:09:22 · answer #2 · answered by DavidK93 7 · 1⤊ 0⤋
It's more common than you might think.
For example, suppose you're solving the equation
x^3 - 2x^2 + x = 0.
You factor out an x, and get x(x^2-2x+1)=0.
If x=0, then the equation is satisfied. If x is nonzero, than you can divide by x, and then solve the equation x^2-2x+1=0.
With variables, as opposed to numbers, you have to assume that the variable is nonzero before dividing by it, and separately handle the scenario where it is zero.
2006-10-11 09:11:11 · answer #3 · answered by James L 5 · 1⤊ 0⤋
take this equation: 9x + 7 = x + 7
subtractring 7 from both sides,
x = 9x
but what if x = 0?
you can't divide by zero.
so you have to recognize the solution without dividing. (not too hard)
2006-10-11 09:35:54 · answer #4 · answered by stop12345now 2 · 0⤊ 0⤋
Because that will generally create a more difficult equation. Also if you are solving an equation for a single variable dividing by the variable will never help you.
Hope this makes sense. Good Luck.
2006-10-11 09:10:04 · answer #5 · answered by SmileyGirl 4 · 0⤊ 2⤋
we do and often it is useful
2006-10-11 09:11:05 · answer #6 · answered by ? 7 · 0⤊ 0⤋