SOLUTION: I have two questions: 1) Simplify the following {{{ 2x+3/(2(x-4))-1/(2(x+2)) }}} 2) Solve the equation if possible {{{ 5*sqrt(x)-sqrt(x-1)=6 }}} Thank you!

Question 207626: I have two questions:
1) Simplify the following

2) Solve the equation if possible

Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Start with the given expression.

Multiply the first fraction by

Multiply the second fraction by

Multiply the third fraction by

FOIL

Multiply

Distribute

Combine the fractions.

Distribute

Combine like terms.

Factor out the GCF 2

Cancel out the common terms.

Simplify

So

# 2

Start with the given equation.

Add to both sides.

Square both sides.

Square the left side.

FOIL the right side.

Square the last term.

Subtract 'x' from both sides.

Combine like terms.

Subtract 35 from both sides.

Square both sides.

Square the right side.

FOIL the left side

Distribute

Get every term to the left side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

or Reduce.

So the possible solutions are or

which approximate to or

However, if you plug in back into the original equation, you'll find a contradiction.

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Answer:

So the only solution is which approximates to