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The phrase "without additional cost" is correct and usable in written English.
You can use it when you want to indicate that something is not associated with an extra charge. For example, you could say: "We're pleased to offer you this service without additional cost."
Exact(36)
After all, either alternative would limit losses without additional cost.
Although single payer enables universal care without additional cost, Dr. Relman notes that it will not slow cost increases.
Brooklyn Generation School replaced most administrators with teachers and staggered all employees' schedules, allowing it to increase learning time by 30 percent without additional cost.
Ms. Gotbaum said the system could be improved without additional cost if it moved dollars away from crisis management services toward preventive services like basic education in child rearing.
None needed reminding of the challenges ahead: meeting the growing demand for care at home in an ageing society; alleviating pressures on carers which damage their health and quality of life; helping carers to combine work and care; and finding ways of providing better, more personal and individual care without additional cost.
In a statement, the airport also said that passengers holding a ticket for a Lufthansa Group flight (Brussels Airlines, Lufthansa, Swiss, Austrian Airlines and Germanwings) between Tuesday and 28 March, to, from or via Brussels could rebook without additional cost or obtain a refund for their ticket.
Similar(24)
Now I can take rooms out without additional costs.
For the special case when t=0, workers can choose any firm without additional costs.
Finally, guidelines and priorities for wind turbine manufacturers, generating entities, balancing authorities and regulators are provided to ensure the increased reliability without additional costs.
However, because each technology component exists in a non-physical form similar to blueprints, it is assumed that its output is duplicated without additional costs.
As productivity increases, we have the ability to produce more goods while maintaining the same inputs, a wonderful outcome because it means we can serve more of our wants without additional costs.
More suggestions(15)
without further cost
without additional investment
without additional burden
without additional charge
without additional maintenance
without additional capital
without additional expense
without extra cost
without additional burdens
without increasing cost
without additional improvement
without additional city
without additional purification
without additional hardware
without additional study
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com