Question 137516
1) Solve for x:
{{{1+(1/x) = 56/x^2}}} Combine the terms on the left side.
{{{(x+1)/x = 56/x^2}}} Multiply both sides by {{{x^2}}}
{{{x^2(x+1)/x = 56}}} Cancel an x on the left side.
{{{x(x+1) = 56}}} Perform the indicated multiplication on the left side.
{{{x^2+x = 56}}} Subtract 56 from both sides.
{{{x^2+x-56 = 0}}} Factor this quadratic equation.
{{{(x-7)(x+8) = 0}}}
{{{x = 7}}}, {{{x = -8}}}
2) Find the LCD of:
{{{(7a+14)}}} and {{{(a^2+2a)}}}
You are to assume that these expressions are the denominators of fractions, so let's write them that way:
{{{x/((7a+14))}}}, {{{y/((a^2+2a))}}} Now we'll find the LCD. Factor the denominators, as you have done:
{{{x/7(a+2)}}}, {{{y/a(a+2)}}} Now you need to make a common denominator, so multiply the first one by a and the second one by 7.
{{{ax/7a(a+2)}}}, {{{7y/7a(a+2)}}} Now you can see that the LCD is:
{{{7a(a+2) = 7a^2+14a}}}