Q78. Solve the equation 2a-5a-9+aa+9=... [FREE SOLUTION]

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Chapter 10: Q78. (page 530)

Solve the equation $\frac{2 a - 5}{a - 9} + \frac{a}{a + 9} = \frac{- 6}{a^{2} - 81}$ . Check your solution.

Short Answer

Expert verified

The solution for the equation is $a = \{3, - \frac{13}{3}\}$ .

Step by step solution

Step 1. Write down the given expression.

The given equation is $\frac{2 a - 5}{a - 9} + \frac{a}{a + 9} = \frac{- 6}{a^{2} - 81}$ .

Step 2. Simplify the equation.

The given equation $\frac{2 a - 5}{a - 9} + \frac{a}{a + 9} = \frac{- 6}{a^{2} - 81}$ is solved as:

$\begin{array}{l} \frac{2 a 鈭� 5}{a 鈭� 9} + \frac{a}{a + 9} = \frac{鈭� 6}{a^{2} 鈭� 81} .... (Given) \\ \frac{2 a 鈭� 5}{a 鈭� 9} + \frac{a}{a + 9} = \frac{鈭� 6}{(a 鈭� 9) (a + 9)} \\ (2 a 鈭� 5) (a + 9) + a (a 鈭� 9) = 鈭� 6 \\ 2 a^{2} + 13 a 鈭� 45 + a^{2} 鈭� 9 a = 鈭� 6 \\ 3 a^{2} + 4 a 鈭� 39 = 0 \end{array}$

Further simplifying,

$\begin{array}{l} 3 a^{2} 鈭� 9 a + 13 a 鈭� 39 = 0.... (Factoring) \\ 3 a (a 鈭� 3) + 13 (a 鈭� 3) = 0 \\ (a 鈭� 3) (3 a + 13) = 0 \\ a 鈭� 3 = 0 or 3 a + 13 = 0 \\ a = 3 or a = 鈭� \frac{13}{3} \\ a = \{3, 鈭� \frac{13}{3}\} \end{array}$

Step 3. Verify the result for obtained value.

Plugging $a = 3$ in given equation and verify the result.

$\begin{array}{l} \frac{2 a 鈭� 5}{a 鈭� 9} + \frac{a}{a + 9} = \frac{鈭� 6}{a^{2} 鈭� 81} .... (Given) \\ \frac{2 (3) 鈭� 5}{(3) 鈭� 9} + \frac{(3)}{(3) + 9} = \frac{鈭� 6}{{(3)}^{2} 鈭� 81} .... (Plugging a = 3) \\ 鈭� \frac{1}{6} + \frac{1}{4} = \frac{鈭� 6}{鈭� 72} \\ \frac{鈭� 2 + 3}{12} = \frac{1}{12} \\ \frac{1}{12} = \frac{1}{12} .... (True) \end{array}$

Hence the solution is verified for $a = 3$ .

Step 4. Conclusion.

The solution for the given equation is $a = \{3, - \frac{13}{3}\}$ .

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91影视

Solve the equation $\frac{2 a - 5}{a - 9} + \frac{a}{a + 9} = \frac{- 6}{a^{2} - 81}$ . Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

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91影视

Solve the equation 2a-5a-9+aa+9=-6a2-81. Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Calculus

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the equation $\frac{2 a - 5}{a - 9} + \frac{a}{a + 9} = \frac{- 6}{a^{2} - 81}$ . Check your solution.