Rational Value Equations

Hey everyone,

Its me m@rk again. We start off today's short class with four questions.

The first question was:

√x+1 +2=4 REMEMBER: The first step is to isolate the radical by itself

√x+1=2 Square both sides to get rid of the radical sign

x+1=4 Subtract 1 on both sides

x=3 REMEMBER: Substitute your answer back at the equation and see if it makes sense.


The second question was:

x=√x+10 +2 Isolate the radical by itself

x-2=√x+10 Square both sides to get rid of the radical sign

(x-2) (x-2)= x+10 Distribute

x^2-4x+4 =x+10 Simplify it to an equation you are comfortable of doing

x^2-5x-6 = 0 Factor to find the roots

(x-6) (x+1) = 0

∴ x= 6,-1

Remember to substitute your answer in the original equation. In this question the
answer of -1 doesnt make sense, because it will not balance the equation. This case is called an extraneous solution.

The third question was:

4/x=3 , X ≠ 0 REMEMBER: WRITE THE RESTRICTIONS

4/x=3 Multiply both sides by the LCD to get rid of the fraction

4=3x

4/3=x Look at your resrictions if its not the same then it is not an extraneous solution


Lastly, the fourth question was:

4/x-3/x+1=1 , x ≠ 0,-1 REMEMBER: State your restrictions

4/x-3/x+1=1 Multiply both sides by the LCD

4x+4-3x =x^2+x Simplify

x^2-4=0 Factor

(x+2) (x-2)=0

∴ x=2,-2 Look back at your restrictions if its not the same, it is not an extraneous solution.

That's it for my scribe for today. Mr. K , we used the rest of the class time to do our homework. The lady was quite impress on how we focused till the last second of the class.

Our homework for tonight is Exercise #19. The next scribe is......... (background music:dun..dun...) the one and only SAMUS or should I say Mz. Anonymous. Good nyt and have fun.....