Consider the example: \(\displaystyle{\frac{{{7}}}{{{x}}}}={0}\) If we multiply both sides

anadyrskia0g5

anadyrskia0g5

Answered question

2022-03-26

Consider the example:
7x=0
If we multiply both sides by x we get
7=0
which obviously is wrong.
However with the equation
7x267x+126x(x2)(x3)=0
You can multiply by zero and get
7x267x+126=0
I think it is because there are still x's remaining in the expression. However what is the exact rule when it is allowed to multiply by zero and when it is not...

Answer & Explanation

Mikaela Winters

Mikaela Winters

Beginner2022-03-27Added 14 answers

In your first case,
7x=0
doesn't have a solution. This is because
yx
is only equal to 0 if y=0
If x=0 the expression is undefined.
In your second case we can deduce that, as the fraction is equal to 0, the numerator must be equal to 0. This gives us
7x267x+126=0
which can then be solved.

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