Then the value of $\frac{3x}{2x^2 + 2 - 5x}$ will be:
Simplifying the Algebraic Expression
We are given the equation $x + \frac{1}{x} = 5$. We need to find the value of the expression $\frac{3x}{2x^2 + 2 - 5x}$.
Evaluating the Expression
First, let's focus on the denominator of the expression: $2x^2 + 2 - 5x$.
We can manipulate this denominator by dividing both the numerator and the denominator of the main expression by x (since $x \neq 0$ from the given equation $x + \frac{1}{x} = 5$):
$ \frac{3x}{2x^2 + 2 - 5x} = \frac{\frac{3x}{x}}{\frac{2x^2}{x} + \frac{2}{x} - \frac{5x}{x}} $
This simplifies to:
$ \frac{3}{2x + \frac{2}{x} - 5} $
Now, we can factor out 2 from the first two terms in the denominator:
$ \frac{3}{2 \left( x + \frac{1}{x} \right) - 5} $
Substituting the Given Value
We know that $x + \frac{1}{x} = 5$. Substitute this value into the simplified expression:
$ \frac{3}{2(5) - 5} $
Final Calculation
Perform the calculation:
$ \frac{3}{10 - 5} = \frac{3}{5} $
Therefore, the value of the expression is $\frac{3}{5}$.
Similar Questions
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- If $3a + 4b = 2$ and $ab = \frac{1}{36}$, then $27a^3 + 64b^3$ is:
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Important Questions from Algebra
If 2x – y = 2 and xy = \(\frac{3}{2}\) , then what is the value of x 3– \(\frac{{{y^3}}}{8}\) ?
If (10a 3+ 4b 3) : (11a 3- 15b 3) = 7 : 5, then (3a + 5b) : (9a - 2b) =?
- If 4sin 2 θ = 3(1+ cos θ), 0° < θ < 90°, then what is the value of (2tan θ + 4sin θ - sec θ)?
The value of:
\(\frac{{\sin 23^\circ \cos 67^\circ + \sec52^\circ \sin38^\circ + \cos 23^\circ \sin 67^\circ + \rm cosec52^\circ \cos 38^\circ }}{{\rm cose{c^2}20^\circ - {{\tan }^2}70^\circ }}\)
If (x + y) 3+ 27(x - y) 3= (Ax - 2y)(Bx 2+ Cxy + 13y 2), then the value of A - B - C is:
