What is the simplified form of the quantity of x plus 4, all over 5 + the quantity of x plus 5, all over 5 ? (2 points) the quantity of x squared plus 9x plus 20, all over 5
the quantity of 2x plus 9, all over 5
the quantity of x squared plus 9x plus 20, all over 25
the quantity of x plus 4, all over the quantity x plus 5

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

if you was gonna solve for a, a is a   < -12