Question

Evaluate x+2x+1/x^2-25

Answer 1

The evaluation of the algebraic fraction x+2x+1/x^2-25 is$\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}$

What is the division of algebraic expression?

The division of an algebraic expression can be carried out by using the long division method or expansion of the.

Given that:

$\mathbf{\dfrac{x+2x+21}{x^2-25}}$

where:

• x^2 - 25 is the divisor.

By expanding the denominator, we have:

$\mathbf{\dfrac{x+2x+21}{(x+5)(x-5)}}$

$\mathbf{\dfrac{3x+21}{(x+5)(x-5)}}$

Creating a partial fraction from the denominator, we have:

$\mathbf{\dfrac{3x+21}{(x+5)(x-5)} = \dfrac{a_o}{x+5} +\dfrac{a_1}{x-5}}$

Multiply the equation by the denominator, and we have:

$\mathbf{\dfrac{(3x+21)(x+5)+(x-5)}{(x+5)(x-5)} = \dfrac{a_o(x+5)(x-5)}{x+5} +\dfrac{a_1(x+5)(x-5)}{x-5}}$

Simplifying, we have:

3x + 21 = a₀(x-5)+a₁(x+5)

Solve for the unknown parameter by plugging the real roots of the denominator: -5, 5

$\mathbf{a_o =\dfrac{-3}{5}}$

$\mathbf{a_1 =\dfrac{18}{5}}$

Replacing the solutions into the partial fractions parameters to obtain the final result, we have:

$\mathbf{\dfrac{-(\dfrac{3}{5})}{x+5} +\dfrac{\dfrac{18}{5}}{x-5}}$

$\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}$

Learn more about the division of algebraic fractions here:

brainly.com/question/24705296

#SPJ1