[tex]\bf \cfrac{\frac{x+4}{3}+\frac{1}{x}}{5+\frac{15}{x}}\qquad \cfrac{\impliedby \frac{LCD}{3x}}{\impliedby \stackrel{LCD}{x}}\implies \cfrac{\quad \frac{x(x+4)+3(1)}{3x}\quad }{\frac{x(5)+(1)15}{x}}\implies \cfrac{\quad \frac{x^2+4x+3}{3x}\quad }{\frac{5x+15}{x}}[/tex]
[tex]\bf \cfrac{x^2+4x+3}{3\underline{x}}\cdot \cfrac{\underline{x}}{5x+15}\implies \cfrac{x^2+4x+3}{3(5x+15)}\implies \cfrac{x^2+4x+3}{15x+45}
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\cfrac{(x+3)(x+1)}{15x+45}\implies \cfrac{\underline{(x+3)}(x+1)}{15\underline{(x+3)}}\implies \cfrac{x+1}{15}[/tex]
