Solving Rational Equation:
The solution of the rational equation: 3/x + 1 = 2/x – 3 is x = 11. One way of solving this rational equation is by using the common denominator which is given by the product of (x + 1)(x – 3). This method is used when the equation to be solved are in fraction form just like 3/x + 1 and 2/x – 3.
Solving Rational Equation: brainly.ph/question/1639804
Solution:
Write the given rational equation: 3/x + 1 = 2/x – 3 .
Multiply both sides of the equation by their common denominator:
(x + 1)(x – 3)[3/x + 1 = 2/x – 3](x + 1)(x – 3)
3. Simplify the equation using distributive property.
3(x – 3) = 2(x + 1)
3x – 3(3) = 2x + 2(1)
3x – 9 = 2x + 2
4. Combine all the similar terms in one side.
3x – 2x = 2 + 9
5. Thus, x = 11.
Remember:
A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials.
In solving rational equations, the fractions must be reduced using a common denominator then proceed to solving the equality of the numerators.
Rational equations can be used to solve a variety of problems that involve rate, time, and work which is helpful in combining machines and workers to finish the job on time.
What are rational equations: brainly.ph/question/1623226
Examples:
1. Solve: 5/2x - 3/4x² = 2/3x
2. Find the common denominator.
(2x)(4x²)(3x)
3. Multiply both sides of the equation by the common denominator.
(2x)(4x²)(3x)[5/2x – 3/4x² = 2/3x] (2x)(4x²)(3x)
5(4x²)(3x) – 3(2x)(3x) = 2(2x)(4x²)
4. Simplify the equation using the distributive property.
5(12x³) – 3(6x²) = 2(8x³)
60x³ – 18x² = 16x³
5. Equate everything to zero.
60x³ – 16x³ – 18x² = 0
44x³ – 18x² = 0
6. Change the answer into its simplest form using common monomial factor.
2x²(22x – 9) = 0
2x² = 0; 22x – 9 = 0
x = √0/2; 22x = 9
7. Thus, x = 0; x = 9/22
Examples of rational equations: brainly.ph/question/2260337 https://brainly.ph/question/855394
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