# Solve Graphically t/(t-2)+4/(t+2)=8/(t^2-4)

tt-2+4t+2=8t2-4
Simplify tt-2+4t+2.
To write tt-2 as a fraction with a common denominator, multiply by t+2t+2.
tt-2⋅t+2t+2+4t+2=8t2-4
To write 4t+2 as a fraction with a common denominator, multiply by t-2t-2.
tt-2⋅t+2t+2+4t+2⋅t-2t-2=8t2-4
Write each expression with a common denominator of (t-2)(t+2), by multiplying each by an appropriate factor of 1.
Multiply tt-2 and t+2t+2.
t(t+2)(t-2)(t+2)+4t+2⋅t-2t-2=8t2-4
Multiply 4t+2 and t-2t-2.
t(t+2)(t-2)(t+2)+4(t-2)(t+2)(t-2)=8t2-4
Reorder the factors of (t-2)(t+2).
t(t+2)(t+2)(t-2)+4(t-2)(t+2)(t-2)=8t2-4
t(t+2)(t+2)(t-2)+4(t-2)(t+2)(t-2)=8t2-4
Combine the numerators over the common denominator.
t(t+2)+4(t-2)(t+2)(t-2)=8t2-4
Simplify the numerator.
Apply the distributive property.
t⋅t+t⋅2+4(t-2)(t+2)(t-2)=8t2-4
Multiply t by t.
t2+t⋅2+4(t-2)(t+2)(t-2)=8t2-4
Move 2 to the left of t.
t2+2⋅t+4(t-2)(t+2)(t-2)=8t2-4
Apply the distributive property.
t2+2t+4t+4⋅-2(t+2)(t-2)=8t2-4
Multiply 4 by -2.
t2+2t+4t-8(t+2)(t-2)=8t2-4
t2+6t-8(t+2)(t-2)=8t2-4
t2+6t-8(t+2)(t-2)=8t2-4
t2+6t-8(t+2)(t-2)=8t2-4
Simplify the denominator.
Rewrite 4 as 22.
t2+6t-8(t+2)(t-2)=8t2-22
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=t and b=2.
t2+6t-8(t+2)(t-2)=8(t+2)(t-2)
t2+6t-8(t+2)(t-2)=8(t+2)(t-2)
Graph each side of the equation. The solution is the x-value of the point of intersection.
t=-8
Solve Graphically t/(t-2)+4/(t+2)=8/(t^2-4)