# 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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