rearranging equation

[Fennic]

Hi forum,

I am trying to rearrange the following equation in terms of d as I then want to interpret the result when Y=90, but I am having some trouble, as wouldn't d^h just cancel out in the equation?

Can anyone assist with this?

 

[MarkFL]

I would first multiply by \(d^h+k^h\) to get:

[MATH]Y(d^h+k^h)=100d^h[/MATH]
Distribute:

[MATH]Yd^h+Yk^h=100d^h[/MATH]
Arrange as:

[MATH]Yd^h-100d^h=-Yk^h[/MATH]
Factor the LHS:

[MATH](Y-100)d^h=-Yk^h[/MATH]
Can you continue?

 

[Dr.Peterson]

I am trying to rearrange the following equation in terms of d as I then want to interpret the result when Y=90, but I am having some trouble, as wouldn't d^h just cancel out in the equation?

Can anyone assist with this?

View attachment 17073

"Canceling" in a fraction doesn't mean merely crossing out anything that appears anywhere in the numerator and the denominator.

It is only allowed when what you are "canceling" is a factor of both parts -- not a term in a sum.

You can't cancel "a" in [MATH]\frac{ab}{a+b}[/MATH] to make [MATH]\frac{b}{b}[/MATH] or [MATH]\frac{b}{1+b}[/MATH], because it is not a factor of the denominator, only of one term in it.

You can cancel "a" in [MATH]\frac{ab}{ac}[/MATH] to make [MATH]\frac{b}{c}[/MATH], because [MATH]\frac{ab}{ac} = \frac{a}{a}\cdot\frac{b}{c} = 1\cdot\frac{b}{c} = \frac{b}{c}[/MATH].