Consider the two expressions $\frac{4x^3+2x^2+6x+7}{2x+1}$ and $2x^2+3+\frac4{2x+1}.$ a) show that the two expressions are equal to each other when $x=10.$ b) explain why these two expressions are not equal to each other when $x=-\dfrac12.$ c) show that these two expressions are equal to each other for all $x$ other than $-\dfrac12.$

During your cycling trip, you and your friends often stayed in hostels. the prices of these are listed below. hostel standard room (price per night) with breakfast (price per night) super sleep hostels £22.45 £28.65 normandy nights £18.55 £25 zzzola hostels £24.50 £30.99 belgian beds £11.20 £18.55 night-time rest days ? £33 what is the range in cost for a single night, including both standard room prices and with breakfast prices?

The graph shows the charges for a health club in a month. make a function table for the input-output values. writes an equation that can be used to find the total charge y for the number of x classes

What is the quotient of m^6/5 ÷ 5/m^2? assume m does not equal pl