tt-2+4t+2=8t2-4

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

Add 2t and 4t.

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

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)