Question 130067
Let n be the required number.
"The reciprocal of 2 more than a number..." can be expressed as:
{{{1/(n+2)}}}
"...three fourths of the reciprocal of the number itself." can be expressed as:
{{{(3/4)(1/n)}}}
Setting these two equal to each other we get:
{{{1/(n+2) = (3/4)(1/n)}}} Simplify.
{{{1/(n+2) = 3/4n}}} Cross-multiply by the denominators.
{{{4n = 3(n+2)}}} Simplify.
{{{4n = 3n + 6}}} Subtract 3n from both sides.
{{{n = 6}}}
The number is 6.

Check:
{{{1/(n+2) = (3/4)(1/n)}}} Substitute n = 6.
{{{1/(n+2) = (3/4)(1/6)}}}
{{{1/8 = 3/24}}}
{{{1/8 = 1/8}}} It checks!