So we are given the equation:
[tex] \frac{(a^{2}+b^{2})(a^{2}-b^{2})}{(a+b)^{2}(2a^{2}-3ab+b^{2})} [/tex]
Then let's plug in 4 for all of the a's and 3 for all of the b's:
[tex] \frac{(4^{2}+3^{2})(4^{2}-3^{2})}{(4+3)^{2}(2(4)^{2}-3(4)(3)+3^{2})} [/tex]
And then we solve using PEMDAS:
[tex] \frac{(16+9)(16-9)}{(7)^{2}(2(16)-3(12)+9)} [/tex]
[tex] \frac{(25)(7)}{49(32-36+9)} [/tex]
[tex] \frac{175}{49(5)} [/tex]
[tex] \frac{175}{245} [/tex]
Then if we divide both the numerator and the denominator by 35, we get: [tex] \frac{5}{7} [/tex]
And thus [tex] \frac{5}{7} [/tex] is the most simplified answer.
