How would you solve this QR?

[sfoksn]

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sqrt(x^2-9) / sqrt(x+3) = 4.

How would you solve for x?

Thanks.

 

[sfoksn]

Represent y = (x+5)/(x-9) in form of x=

 

[RSD2014]

sqrt(x^2-9) / sqrt(x+3) = 4.

How would you solve for x?

Thanks.

x = 19

 

[JBarr29]

wouldnt x just be = to 19?

 

[UndergradGuy7]

wouldnt x just be = to 19?

This is what I got. The solution RSD did you need to do the quadratic and I didn't get the same answer as him. What you can do instead is factor.

Like so
sqrt(x^2-9) / sqrt(x+3) = 4
or
(x^2-9)^(1/2) / (x+3)^(1/2) = 4
If you factor the top you get [(x-3)^(0.5) * (x+3)^(0.5) ]/ (x+3)^(0.5) = 4
The (x+3)^(0.5) cancel. You get (x-3)^0.5 = 4
Square both sides
x-3 = 16
x=19

 

[sfoksn]

y = (x+4)/(x+6). What is x =

 

[UndergradGuy7]

y = (x+4)/(x+6). What is x =

Multiply by (x+6) on each side.
👍*(x+6) = (x+4)
distribute left side yx +6y = (x+4)
Make all parts of the equation with x on one side and everything else on the other side.
6y -4 = x -yx
Factor the right side
6y - 4 = (1-y) * x
Now this goes to (6y-4)/(1-y) = x


Did you still need this one solved Represent y = (x+5)/(x-9) in form of x= ?
It is the same as the one above I think.

 

[sfoksn]

Wow, thank you so much.

I didn't know it could be done so simply.

How are you doing in QR section? you must be doing well

 

[UndergradGuy7]

I haven't started that yet. I touched up on some Gen Chem and doing Bio now. I am pretty good at Algebra, but kinda rusty on trig.

 

[sfoksn]

when are you going to be taking your DAT?

 

[UndergradGuy7]

End of May hopefully, if I finish studying everything. But it is annoying studying during classes. Can only study DAT stuff 2 days a week or so.