Solve and check: 1/(x + 3) = (x + 10)/(x - 2) from least to greatest, the solutions are x = ? and x = ?
Solution:
Follow the steps below:
Step 1: Multiply both sides by (x + 3) and (x - 2).
⇒ [(x + 3) × (x - 2) × 1]/ (x + 3) = [(x + 3) × (x - 2) × (x + 10)] / (x - 2)
Step 2: Simplify both sides.
⇒ 1 × (x - 2) = (x + 10) × (x + 3)
⇒ x - 2 = x² + 3x + 10x + 30
⇒ x² + 13x + 30 - x + 2 = 0
⇒ x² + 12x + 32 = 0
Step 3: Factorise the quadratic equation by splitting the middle term.
⇒ x² + 12x + 32 = 0
⇒ x² + 8x + 4x + 32 = 0
Step 4: Take out common terms.
⇒ x (x + 8) + 4 (x + 8) = 0
⇒ (x + 8) (x + 4) = 0
Step 5: Evaluate for x equating the factors to zero.
(x + 8) = 0 or x = - 8
(x + 4) = 0 or x = - 4
Thus the solutions from least to greatest after solving the given equation = x = - 4 , - 8
Solve and check: 1/(x + 3) = (x + 10)/(x - 2) from least to greatest, the solutions are x = ? and x = ?
Summary:
The solutions are x = - 4 and x = - 8, if 1/(x + 3) = (x + 10)/(x - 2) from least to greatest.
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