Verified Answer :

Panoyin

\(\frac{x + 8}{x + 2} + \frac{x - 3}{4} = \frac{4(x + 8)}{4(x + 2)} + \frac{(x + 2)(x - 3)}{4(x + 2)} = \frac{4(x) + 4(8)}{4(x + 2)} + \frac{x(x - 3) + 2(x - 3)}{4(x + 2)} = \frac{4x + 32}{4(x + 2)} + \frac{x(x) - x(3) + 2(x) - 2(3)}{4(x + 2)} = \frac{4x + 32}{4(x + 2)} + \frac{x^{2} - 3x + 2x - 6}{4(x + 2)} = \frac{4x + 32}{4(x + 2)} + \frac{x^{2} - x - 6}{4(x + 2)} = \frac{(4x + 32) + (x^{2} - x - 6}{4(x + 2)} = \frac{x^{2} + (4x - x) + (32 - 6)}{4(x + 2)} = \frac{x^{2} + 3x + 26}{4(x + 2)}\)

Answer:  \(\frac{x^2+3x+26}{4x+8}\)

Step-by-step explanation:

Since, according to the question the given expression,

\(\frac{x+8}{x+2} + \frac{x-3}{4}\)

=\(\frac{4(x+8)+(x-3)(x+2)}{4(x+2)}\)

=\(\frac{4x+32+(x-3)(x+2)}{4x+8}\) (By solving the parenthesis )

=\(\frac{4x+32+x(x+2)-3(x+2)}{4x+8}\) ( by distributive property)

=\(\frac{4x+32+x^2+2x-3x-6}{4x+8}\) ( again on applying distributive property)

=\(\frac{3x+26+x^2}{4x+8}\) ( by operating like terms)

=\(\frac{x^2+3x+26}{4x+8}\)


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