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Solve the rational equation and make sure to check for extraneous solutions 3/x+3=4/x-4

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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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