Solving Equation Problems w/ Componendo & Dividendo

[1/2"]

Hey this is worked out sum from my book and I am having a bit problem in understanding it

Homework Statement

(It's a pure quadratic equation)
If (35-2x)/9+(5x ²+7)/(5x ²-7)=(17-2/3x)/3 find x

Well its worked out well till
(5x ²+7)/(5x ²-7)=16/9
and the comes the real confusion is
Its given
5x ²/7= (16+9)/(16-9)=25/7 [componendo and dividendo]
What is this" componendo and dividendo"?
I don't know !Please help!

Another e.g. is
√( 3x^2-7x-30)-√(2x^2-7x-5)=x-5
then they write
Identically
(3x^2-7x-30)-2x^2-7x-5)=x^2-25(!?)
Is this also by the same" componendo and dividendo"?
Plz help me out! I really don't this componendo and dividendo !

 

[Mark44]

Hey this is worked out sum from my book and I am having a bit problem in understanding it

Homework Statement

(It's a pure quadratic equation)
If (35-2x)/9+(5x ²+7)/(5x ²-7)=(17-2/3x)/3 find x

Well its worked out well till
(5x ²+7)/(5x ²-7)=16/9
and the comes the real confusion is
Its given
5x ²/7= (16+9)/(16-9)=25/7 [componendo and dividendo]
What is this" componendo and dividendo"?
I don't know !Please help!

It means composing and dividing. Are you studying a math book in Spanish?

The equation below is fine.
(5x ²+7)/(5x ²-7)=16/9
I don't follow what you have in the equation below that one, but if you continue working on the equation above you should be able to arrive at the solution(s). Multiply both sides by 9(5x² -7).

Another e.g. is
√( 3x^2-7x-30)-√(2x^2-7x-5)=x-5
then they write
Identically
(3x^2-7x-30)-2x^2-7x-5)=x^2-25(!?)
Is this also by the same" componendo and dividendo"?
Plz help me out! I really don't this componendo and dividendo !

Where are you getting this stuff? Is this from some other student? Whatever, this isn't how you solve equations like this. You can't get to the 2nd equation from the first equation. It looks like whoever did this squared each term on the left side (which is not a valid operation), and then incorrectly squared each term on the right side. This is totally bogus.

 

[1/2"]

I think so too and I'm going nuts over it .
anyawy thanks A LOT!