solve equation if equation has no solution state so,simply when necessary
2/3x+1x=1/6
1/x+4-1/x-2=x+2/x^2+2x-8
help me please
1. 2/3+1= 1/2/3
1/2/3x=1/6
X=1/10
2.i don't get it sry
hard to tell what your equation is, since you did not use brackets.
I have a feeling the second one might be
1/(x+4) - 1/(x-2) = (x+2)/(x^2 + 2x - 8)
the denominator on the right side factors to (x+4)(x-2) which shows up on the left, so multiply each term by (x+4)(x-2) to get
(x-2) - (x+4) = x+2
x-2 -x - 4 = x+2
-6 = x+2
x = -8
retype the first one using brackets
2/3x+1/x=1/6
it does not have bracket in the book.this is how it done. it 2 over 3x plus 1 over x equal 1 over 6.
To solve the equations, we'll follow these steps:
1. Rearrange the equations.
2. Combine like terms.
3. Eliminate any fractions.
4. Simplify the equations.
5. Solve for x.
Let's begin with the first equation:
1. 2/3x + 1x = 1/6
To combine the two terms on the left side, we need a common denominator:
2. (2/3)x + x = 1/6
To find a common denominator, multiply the first term by 2/2:
3. (2/3)x + (2/2)x = 1/6
4. (2/3)x + (4/6)x = 1/6
Combining the terms on the left side:
5. (6/6)x = 1/6
Since the denominators are the same, we can equate the numerators:
6. 6x = 1
Now, let's solve for x:
7. Divide both sides of the equation by 6:
8. x = 1/6
So, the solution for the first equation is x = 1/6.
Moving on to the second equation:
1. 1/x + 4 - 1/x - 2 = x + 2/x^2 + 2x - 8
Combine like terms on the left side:
2. (1/x - 1/x) + 4 - 2 = x + (2/x^2) + 2x - 8
Simplify:
3. 4 - 2 = x + (2/x^2) + 2x - 8
Combine like terms:
4. 2 = 3x + (2/x^2) - 6
Multiply through by x^2 to eliminate the fraction:
5. 2x^2 = 3x(x^2) + 2(x^2) - 6x^2
Simplify:
6. 2x^2 = 3x^3 + 2x^2 - 6x^2
Combine like terms:
7. 2x^2 = 3x^3 - 4x^2
Rearrange:
8. 3x^3 - 6x^2 + 2x^2 - 4x^2 = 0
Combine like terms:
9. 3x^3 - 8x^2 = 0
Factor out x^2:
10. x^2(3x - 8) = 0
This equation can be true if either x^2 = 0 or 3x - 8 = 0. Let's solve those separately:
For x^2 = 0:
11. x = 0
For 3x - 8 = 0:
12. 3x = 8
13. x = 8/3
Therefore, the solutions for the second equation are x = 0 and x = 8/3.
If an equation has no solution, it means that there is no value of x that satisfies the equation.