Question

Solve for x = 1/x+4 - 1/x-7 =11/30

Answer 1

1/x+4 - 1/x-7 = 11/30, x ≠ -4, 7

Move constant to the left

☛ 1/x+4 - 1/x-7 - 11/30 = 0

Write all the numerators above the common denominators

☛ 30(x - 7) - 30(x + 4) - 11(x + 4) × (x - 7)/30(x + 4) × (x - 7) = 0

Remove the brackets

☛ 30x - 210 - 30x - 120 + (-11x - 44) × (x - 7)/30(x + 4) × (x - 7) = 0

Eliminate the oposites and remove the brackets

☛ -210 - 120 - 11x² + 77x - 44x + 308/3(x + 4) × (x - 7) = 0

Calculate and collect the like terms

☛ -22 - 11x² + 33x/30(x + 4) × (x - 7) = 0

Set the numerator equal to 0

☛ -22 - 11x² + 33x = 0

Reorder the terms

☛ -11x² + 33x - 22 = 0

Divide both the sides by -11

☛ x² - 3x - 2 = 0

Solve the quadriatic equation

☛ x = -(-3) ± √[(-3)² - 4 × 1 × 2]/2 × 1

Calculate and remove the brackets

☛ x = 3 ± √[9 - 8]/2

Subtract the numbers

☛ x = 3 ± √[1]/2

Calculate the root

☛ x = 3 ± 1/2

Separate the solutions

☛ x = 3 + 1/2 or x = 3 - 1/2

Simplify the expressions

☛ x = 2 or x = 1, x ≠ -4, 7

Check if the solutions is in the defined range

☛ x = 2 or x = 1

∴ The final solutions are

$x_1 = 2 \: or \: x_2 = 1$

Answer 2

Answer:

Refer to the attachment below

Step-by-step explanation:

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