please help if you can.
Solve ∆ABC, a = 2.5 cm, c = 3.6 cm, and ∠A = 43°. Begin by sketching and labelling
a diagram. Account for all possible solutions. Express each angle to the nearest
degree and each length to the nearest tenth of a unit.

Simplify the rational expression. No need to state restrictions. [5]
[TIP: expand and simplify the numerator, leave the denominator in factored form]
5 −
2 + − 4 ) − 4 + )
4 ) − ) ÷ 3 + 15
6 ) − − )

The missing side and angles are b = 3.1, <B = 58 and <C = 79 and the simplified expression of [5m - n]/[2m + n] - [4m^2 - 4mn + n^2]/[4m^2 - n^2] ÷ [3n + 15m]/[6m^2 - mn - n^2] is [5m - n]/[2m + n] - [1]/[2m + n] * [(3m + n)]/[3(n + 5m)]

How to solve the triangle ABC?

The given parameters are:

a = 2.5 cm, c = 3.6 cm, and ∠A = 43°

See attachment for the sketch

Calculate the angle C using the following law of sines

a/sin(A) = c/sin(C)

So, we have:

2.5/sin(43) = 3.6/sin(c)

This gives

sin (c) = 3.6 * sin(43 deg)/2.5

Evaluate the product and quotient

sin (c) = 0.9821

Take the arc sin

<C = 79

The measure of angle b is

<B = 180 - 79 - 43

Evaluate

<B = 58

Calculate the side B using the following law of sines

a/sin(A) = b/sin(B)

So, we have:

2.5/sin(43) = b/sin(58)

This gives

b = 2.5 * sin(58 deg)/sin(43 deg)

Evaluate the product and quotient

b = 3.1

Hence, the missing side and angles are b = 3.1, <B = 58 and <C = 79

Simplify the rational expression

The expression is:

[5m - n]/[2m + n] - [4m^2 - 4mn + n^2]/[4m^2 - n^2] ÷ [3n + 15m]/[6m^2 - mn - n^2]

Factorize the expressions

[5m - n]/[2m + n] - [(2m -n)(2m -n)]/[(2m - n)(2m + n)] ÷ [3(n + 5m)]/[(2m- n)(3m + n)]

Cancel out the common factors

[5m - n]/[2m + n] - [2m -n]/[2m + n] ÷ [3(n + 5m)]/[(2m- n)(3m + n)]

Express as product

[5m - n]/[2m + n] - [2m -n]/[2m + n] * [(2m- n)(3m + n)]/[3(n + 5m)]

Cancel out the common factors

[5m - n]/[2m + n] - [1]/[2m + n] * [(3m + n)]/[3(n + 5m)]

Hence, the simplified expression of [5m - n]/[2m + n] - [4m^2 - 4mn + n^2]/[4m^2 - n^2] ÷ [3n + 15m]/[6m^2 - mn - n^2] is [5m - n]/[2m + n] - [1]/[2m + n] * [(3m + n)]/[3(n + 5m)]