+0  
 
0
314
1
avatar

what is the solution set for z/z-5+5/z+5=50/z^2-25

Guest Apr 9, 2017
 #1
avatar+7266 
+3

I think this isn't your question:

\(\frac{z}{z}-5+\frac{5}{z}+5=\frac{50}{z^2}-25\)

 

I think this is your question:

\(\frac{z}{z-5}+\frac{5}{z+5}=\frac{50}{z^2-25}\)

Here, take note of what z values cause a zero in the denominator.

z ≠ 5, z ≠ -5

 

Get a common denominator on the left side

\(\frac{z(z+5)}{(z-5)(z+5)}+\frac{5(z-5)}{(z-5)(z+5)}=\frac{50}{z^2-25}\)

 

Factor the denominator on the right side.

\(\frac{z(z+5)}{(z-5)(z+5)}+\frac{5(z-5)}{(z-5)(z+5)}=\frac{50}{(z-5)(z+5)}\)

 

Multiply through by (z-5)(z+5).

\(z(z+5)+5(z-5)=50\)

 

Distribute and combine like terms.

\(z^2+5z+5z-25=50 \\ z^2+10z-75=0\)

 

Factor and set each factor = 0.

\(z^2+10z-75=0 \\ (z+15)(z-5)=0\)

z+15 = 0     or    z-5 = 0

z = -15        or     z = 5

 

HOWEVER...in the original problem, z = 5 causes a zero in the denominator.

So, z cannot = 5.

The solution set is just: { -15 }

hectictar  Apr 10, 2017

45 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.