Answer:
3. [tex]2a^2-3ab-b^2=0[/tex]
4. [tex]2b=c[/tex]
Solution for number 3 steps:
Hey there!
In order to solve this equation, we are going to cross multiply
To do this, you need to take [tex]-\frac{4a}{a+b}[/tex] to the other side of the equation
It will look like this now
[tex]\frac{2b}{a-b} =\frac{4a}{a+b}[/tex]
Now what we do is cross multiply
We take the a+b and multiply it by 2b and take the a-b and multiply it by 4a
Now the equation looks like this:
[tex]2b^2+2ba=4a^2-4ab[/tex]
Now as you can see, the whole equation is divisible by 2 so we divide the whole equation by 2
Now the equation looks like this:
[tex]b^2+ba=2a^2-2ab[/tex]
We can simplify this even more by taking "ba" to the other side
Now the equation looks like this:
[tex]b^2=2a^2-3ab[/tex]
Now the question is asking us to simplify as much so just to make the equation to look more tidy, we should move everything to one side:
[tex]0=2a^2-3ab-b^2[/tex]
Or
[tex]2a^2-3ab-b^2=0[/tex]
Solution for number 4 steps:
Now we need to solve for number 4
In order to solve this, we can do the same thing that we did with the previous equation, we cross multiply
[tex]\frac{2}{2b-c} +\frac{3}{b-c}[/tex]
But first, as you can see, we can simplify the first fraction
it goes from [tex]\frac{2}{2b-c}[/tex] to [tex]\frac{1}{b-c}[/tex] since we can cancel the 2 out from the numerator and the denominator
now we can rearrange the equation so we can cross multiply
[tex]\frac{1}{b-c}=-\frac{3}{b-c}[/tex]
after cross multiplying, the result will look like this:
[tex]b-c=-3b+c[/tex]
now we can comfortably simplify the equation:
[tex]4b=2c[/tex] ---> [tex]2b=c[/tex]
So the answer for this question would be [tex]2b=c[/tex]
