Chapter 7: Q. 7.78 (page 690)

Solve: $\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6}$

Short Answer

Expert verified

There is no solution.

Step by step solution

Step 1. Given.

The given equation is: $\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6}$

Step 2. To find

We have to solve the given equation.

Step 3. Calculation

$\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6} \frac{5}{(x + 3) (x - 1)} - \frac{3}{(x + 2) (x - 1)} = \frac{1}{(x + 2) (x + 3)} LCMofthedenominators = (x - 1) (x + 2) (x + 3) . So, x - 1 \neq 0 or x \neq 1 And x + 2 \neq 0 or x \neq - 2 And x + 3 \neq 0 or x \neq - 3 Multiplybothsidesby (x - 1) (x + 2) (x + 3) . \frac{5}{(x + 3) (x - 1)} - \frac{3}{(x + 2) (x - 1)} = \frac{1}{(x + 2) (x + 3)} \frac{5}{(x + 3) (x - 1)} (x - 1) (x + 2) (x + 3) - \frac{3}{(x + 2) (x - 1)} (x - 1) (x + 2) (x + 3) = \frac{1}{(x + 2) (x + 3)} (x - 1) (x + 2) (x + 3) 5 (x + 2) - 3 (x + 3) = x - 1 5 x + 10 - 3 x - 9 = x - 1 2 x + 1 = x - 1 2 x - x = - 1 - 1 x = - 2 But, x \neq - 2 . Sothereisnosolution.$

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Solve: $\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6}$

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

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Solve: 5x2+2x-3-3x2+x-2=1x2+5x+6

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve: $\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6}$