## Algebra: A Combined Approach (4th Edition)

$x=1$ or $x=5$
Step 1: We denote the unknown number by $x$. Step 2: The reciprocal of x is $\frac{1}{x}$. Step 3: 'One number plus five times its reciprocal is equal to six' means that $x+5(\frac{1}{x})=6$ $x+(\frac{5}{x})=6$ $(x\times\frac{x}{x})+(\frac{5}{x}\times\frac{1}{1})=6$ $\frac{x^{2}}{x}+\frac{5}{x}=6$ $\frac{x^{2}+5}{x}=6$ ${x^{2}+5}=6x$ $x^{2}-6x+5=0$ $x^{2}-1x-5x+5=0$ $x(x-1)-5(x-1)=0$ $(x-1)(x-5)=0$ $x=1$ or $x=5$.