Whats the difference between equivalent fractions and simplified fractions

A simplified fraction is a fraction in it's simplest form. An equivalent fraction is a fraction that has different numerators and denominators that represent the same value as another fraction. For example, 5/10 in it's simplest form is 1/2, and 8/88 is equivalent to 9/99 because they both have the decimal form of .90 repeating.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the correct option is b

step-by-step explanation: