Question

Simplify the expression: (x^2-4x)/2+√x
Please show complete solution and answer

Answer 1

Multiply by the conjugate

Answer 2

Do you have an idea of what a conjugate is?

Answer 3

@Yttrium yes i do, i tried solving it already. i just wanna know if my answer is correct. my answer is -x(2-√x)

Answer 4

I don't know what a conjugate is, would someone mind explaining?

Answer 5

You even have a difference of squares option for the numerator:
\[\frac{ x(x-4) }{ 2+\sqrt{x} } \]

Now for the top part, that factor of x-4 can be turned into a difference of squares. When you have a - b, whatever a and b are, you can factor it like this:
\[(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})\]And since you already have a solution, Ill work it out a little. So following the above form, I can make x-4 into:
\[(\sqrt{x}+\sqrt{4})(\sqrt{x}-\sqrt{4})= \]
\[(\sqrt{x}+2)(\sqrt{x}-2)\]Now I'll rewrite this as:
\[\frac{ x(\sqrt{x}+2)(\sqrt{x}-2) }{ 2+\sqrt{x} }\]Now we have a factor on bottom and top that cancel"
\[x(\sqrt{x}-2)\]Which, can actually be rewritten in the way you have it by factoring out a negative:
\[-x(-\sqrt{x}+2) or-x(2-\sqrt{x})\]

Answer 6

Psymon stop giving away answers xD

Answer 7

She had the answer already, geez!

Answer 8

Calm down bud :3

Answer 9

I am :P

Answer 10

I just wanted to troll and not use the conjugate xD

Answer 11

Nice job xD

Answer 12

A conjugate is basically when you take the same expression you have, but change the sign in the middle. It's a technique often used for either eliminating square roots and complex numbers or simply rearranging things into something factorable. So for this problem, the conjugate that would have been used would be of the bottom. The conjugate would have been:
\[2-\sqrt{x} \]which is simply the denominator with thesign inthe middle flipped. The strategy is to multiply both the top and the bottom of the fraction by this conjugate like so:
\[\frac{ x(x-4)(2-\sqrt{x}) }{ (2+\sqrt{x})(2-\sqrt{x}) }\]Ill work on the top portion later, the main thing I want fixed is the denominator. So if I foil out the denominator, I'll get this:
\[\frac{ x(x-4)(2-\sqrt{x}) }{ 4-x }\]Now we can do one small thing to allow the bottom to cancel out with the top. If I factor a negative out of the bottom factor, I can get this:

\[\frac{ x(x-4)(2-\sqrt{x}) }{ -(x-4) }\]THose factors now cancel and the negative gets tacked on for a final answer of:
\[-x(2-\sqrt{x})\]This would be the way to go about it. I was just being all sneaky algebra with my difference of squares thing

@gypsy1274

Answer 13

Thanks. And I appreciate seeing two ways of answering the question. :-)

Answer 14

Yeah, absolutely : )