# Thread: Using substitution to solve

1. ## Using substitution to solve

I have two problems...

$({{x+5}\over{x}})^{1\over2}+4({{x}\over{x+5}})^{1\ over2}=4$

$\sqrt{3x+4}+\sqrt{x-4}=2\sqrt{x}$

My teacher said substitution is preffered, but I only seem to make it more complicated. If substitution is not possible, solve regularly.

Can you get me started? Thanks!

2. Originally Posted by nathan02079
I have two problems...

$({{x+5}\over{x}})^{1\over2}+4({{x}\over{x+5}})^{1\ over2}=4$

$\sqrt{3x+4}+\sqrt{x-4}=2\sqrt{x}$

My teacher said substitution is preffered, but I only seem to make it more complicated. If substitution is not possible, solve regularly.

Can you get me started? Thanks!
This should get you started:

1) Substitute $t = \left(\frac{x+5}{x}\right)^{\frac12}$, and you will get a quadratic...

2) Just try squaring both sides, you will see the magic