HELP?!
Equations With Rational Expressions;
1. 5/2y+6 + 1/y-2 = 3/y+3
2. 5/a-5 - 1 = a/a-5
3. 2/x^2-x-12 - 6/x+4 = 2/x-3
4. 65-n/n = 4 + 5/n
5. a/ a-2 + 2/3 = 2/a-2
6. x-1/3 + x+2/4 =1/6
7. 5/3x - 1/9 = 1/x
8. 3/3x-2 = 4/2x+1
9. 3/x+3 - 1/x-2 = 5/2x+6
The way you typed your equations makes them much too ambiguous.
e.g. #2
is it 5/a - 5 - 1 = a/a - 5 the way your typed it, or is it
5/(a-5) - 1 = a/(a-5)
I supect it is the latter.
so multiply each term by the LCD, which would be a-5 to get
5 - 1(a-5) = a
5 - a + 5 = a
-2a =-10
a = -5
clarify the others before I proceed
Try these yourself, remember by multiplying by the LCD, all fractions will disappear.
1. 5/(2y+6) + 1/(y-2) = 3/(y+3)
2. 5/(a-5) - 1 = a/(a-5)
3. 2/(x^2)-x-12 - 6/(x+4) = 2/(x-3)
4. 65-n/(n) = 4 + 5/(n)
5. a/ (a-2) + 2/(3) = 2/(a-2)
6. x-1/(3) + x+2/(4) =1/(6)
7. 5/(3x) - 1/(9) = 1/(x)
8. 3/(3x-2) = 4/(2x+1)
9. 3/(x+3) - 1/(x-2) = 5/(2x+6)
* " / " That Is Suppose to be a fraction line.
some are still ambigious,
e.g. #4 and #6
is #6 (x-1)/3 + (x+2)/4 = 1/6 ???
there is no need to place brackets around the 3 or the 4, but they are needed at the top.
(x-1)/3 + (x+2)/4 = 1/6
multiply each term by 12, which is the LCD for 3,4, and 6
4(x-1) + 3(x+2) = 2
4x-4+3x+6=2
7x = 0
x = 0
try some of the others, let me know what you got
To solve equations with rational expressions, follow these steps:
1. Find a common denominator for all the fractions involved in the equation. The common denominator is the least common multiple (LCM) of the denominators in the equation. This step ensures that all fractions have the same denominator.
2. Multiply every term in the equation by the common denominator found in step 1. This step eliminates the denominators in each fraction.
3. Simplify and combine like terms on both sides of the equation.
4. Solve the resulting equation for the variable.
Let's solve the first equation as an example:
1. Equation: 5/(2y+6) + 1/(y-2) = 3/(y+3)
2. Common denominator: The denominators are (2y+6), (y-2), and (y+3). The LCM of these three expressions is (2y+6)(y-2)(y+3).
3. Multiply every term in the equation by the common denominator:
(2y+6)(y-2)(y+3) * 5/(2y+6) + (2y+6)(y-2)(y+3) * 1/(y-2) = (2y+6)(y-2)(y+3) * 3/(y+3)
Simplifying:
5(y-2)(y+3) + (2y+6)(y+3) = 3(2y+6)(y-2)
Expanding and combining like terms:
5y^2 + 15y - 10 + 2y^2 + 12y + 18 = 6y^2 - 12
Simplifying further:
7y^2 + 27y + 6 = 6y^2 - 12
4. Move all terms to one side to set the equation equal to zero:
7y^2 + 27y + 6 - 6y^2 + 12 = 0
Simplifying:
y^2 + 27y + 18 = 0
You can continue solving this quadratic equation using factoring, completing the square, or the quadratic formula, depending on your preference and the complexity of the equation.