result from nominator

[petr]

Hello,

I ve got an equation:
e^x(2x-1) / [2x*sqrt(x)] = 0

In the solution part of my book I can see they take the nominator e^x(2x-1) and just come up with result e^x=0 or 2x-1 = 0. Why they can ignore the denominator? How it works? thank you.

 

[Deleted member 4993]

Hello,

I ve got an equation:
e^x(2x-1) / [2x*sqrt(x)] = 0

In the solution part of my book I can see they take the nominator e^x(2x-1) and just come up with result e^x=0 or 2x-1 = 0. Why they can ignore the denominator? How it works? thank you.

You are missing grouping symbols []. Without those, your problem changes meaning! So go back and edit your original post!!

Can you think of a value of the denominator - that will make whole expression '= 0"?

 

[petr]

You are missing grouping symbols []. Without those, your problem changes meaning! So go back and edit your original post!!

Can you think of a value of the denominator - that will make whole expression '= 0"?

x=0 would make it all zero.

 

[ksdhart2]

x=0 would make it all zero.

I'd double check the math on that one... We have:

$\displaystyle f(x)=\dfrac{e^x \cdot (2x-1)}{2x \cdot \sqrt{x}}$

Plugging in 0 gives:

$\displaystyle f(0)=\dfrac{e^0 \cdot (2(0)-1)}{2(0) \cdot \sqrt{0}} = \text{???}$

In the solution part of my book I can see they take the [numerator] e^x(2x-1) and just come up with result e^x=0 or 2x-1 = 0. Why they can ignore the denominator?

It might help to think of it in this way. Your original expression says that:

$\displaystyle f(x)=\dfrac{e^x \cdot (2x-1)}{2x \cdot \sqrt{x}}=e^x \cdot (2x-1) \cdot \dfrac{1}{2x \cdot \sqrt{x}}=0$

Now, can you see why, unless the expression is undefined, the value of the denominator is irrelevant? As a hint, consider the Zero Product Property.

 

[Harry_the_cat]

Hello,

I ve got an equation:
e^x(2x-1) / [2x*sqrt(x)] = 0

In the solution part of my book I can see they take the nominator e^x(2x-1) and just come up with result e^x=0 or 2x-1 = 0. Why they can ignore the denominator? How it works? thank you.

In simple terms, a fraction is equal to 0 if the numerator = 0 as long as the denominator doesn't.

That is: As long as a doesn't = 0:

0/a = 0
a/0 is undefined
0/0 is indeterminate