algebra solving rational equations?

Question

First problem: a+3/a=12/a. The a stands alone then +3/a. Second: x -21/x=4. This problem x is by itself then -21/x=4z. Third: is 2b/(b+1)=2-5/2b. Again 2 is by itself then -5/2b. the answers are #1. 3,-3 #2. 7,-3 #3. -5 Im having a very had time understanding how to solve. Hope i explained this well...thanks

Answer 1

There are a couple of ways to do these. One way is to find the least common denominator for all the fractions in the problem, then multiply each fraction by that LCD, which cancels out all the denominators. Example 1: the LCD is 1a

a/1 + 3/a = 12/a

1a(a/1) + 1a(3/a) = 1a(12/a) becomes

a^2 + 3 = 12

a^2 = 9

a = 3 or -3

The other way is to move the fractions with common denominators to the same side of the equal sign, combine them then cross multiply. Example 2:

x - 21/x = 4

-21/x = 4 - x

-21/x = (4-x)/1

-21(1) = x(4-x)

-21 = 4x - x^2

x^2 - 4x - 21 = 0, and do FOIL

Answer 2

1)a+3/a=12/a. Taking 3/a to the other side
and simplifying the rhs, we get :
a=9/a or a^2=9. So a=+3 or -3 Answer.
2) x -21/x=4.
Multiplying both sides by x (assuming x different from zero), we get x^2 - 21 = 4x.
We write it as: x^2 - 4x -21 =0.
Solving this quadratic Eq., we get:
x=7 or -3. Answer.
3)2b/(b+1)=2-5/(2b),
Multiplying both sides by 2b(b+1) ( we assume that b is different from zero and - 1), we get:
4b^2=4b(b+1) - 5(b+1) which leads to
4b^2 =4b^2 - b -5. which gives
b=-5 Answer. Verified.
4b=5 or b=5/4 Answer.

Answer 3

a+(3/a)=12/a
=> (a^2+3)/a=12/a
=>a^2+3=12
=>a^2=12-3=9
=> a= +-3 ans.
x-(21/x)=4
=>(x^2-21)/x=4
=>x^2-21=4x {by cross-multiplication]
=>x^2-4x-21=0
=>(x-7)(x+3)=0
=> x=7 or -3
2b/(b+1)=2-(5/2b)
=> 2b/(b+1)=(4b-5)/2b
=>4b^2-5b+4b-5=4b^2
=> -b=5
=>b= -5

Answer 4

Multiply both factors by z 14=9z-z^2 bypass 14 to the distinct section 0=-14+9z-z^2 multiply by -a million z^2-9z+14=0 ingredient (z-2)(z-7)=0 set each and each quantity equivalent to 0 and medical take care of z z-2=0 z=2 z-7=0 z=7 choose this helps

Answer 5

1. a^2+3=12
.....a^2=9
.....a=+3/-3

2. x^2-21=4x
.....x^2-4x-21=0
.....(x-7)*(x+3)=0
.....x=7,-3

3. 4b^2/(b+1)=4b-5
.....4b^2=(4b-5)*(b+1)
.....4b^2=4b^2-b-5
.....b=-5